chapter 10 math G7

Dropdown

​ ​

Select answer

a number finds the product of that number and itself.

Dropdown

​ ​ ​

Select answer

​ a number finds the factor of a given number that multiplies by itself.

Match

Match the following numbers to their squares.

• 11

• 12

• 13

• 14

• 15

121

144

169

196

225

• 121

• 144

• 169

• 196

• 225

Match

Match the following numbers to their square roots.

• 49

• 64

• 81

• 36

• 25

7

8

9

6

5

• 7

• 8

• 9

• 6

• 5

Multiple Choice

When would it be appropriate to use the $$\pm$$  symbol?

• $$x^2=16$$  

• $$\sqrt[]{16}$$  

• $$4^2=x$$  

• $$\left(-4\right)^2=x$$  

Multiple Choice

True or False?

$$4^2=-4^2$$  

• True

• False

Multiple Choice

True or False?

$$4^2=\left(-4\right)^2$$  

• True

• False

Multiple Choice

True or False?

$$4^2=-\left(4\right)^2$$  

• True

• False

Multiple Choice

$$\sqrt[]{9}=$$  

• 3

• -3

• $$\pm$$  3

• 81

Multiple Choice

If $$x^2=9$$ , then $$x=$$   

• 3

• -3

• $$\pm$$  3

• 81

Multiple Choice

What is 11 squared?

11²

• 132

• 144

• 121

• 22

Multiple Choice

What is 64 squared?

64²

• 4096

• 8

• 16

• 128

Multiple Choice

What is 5 squared?

5²

• 2.5

• 25

• 125

• 10

Multiple Choice

What is the square root of 100?

√100

• 10

• 200

• 50

• 1000

Multiple Choice

What is the square root of 36?

√ 36

• 4

• 6

• 18

• 1296

Multiple Choice

What is 16 squared?

• 8

• 256

• 4

• 32

Multiple Choice

What is the square root of 81?

• 3

• 162

• 6561

• 9

Multiple Choice

What is 25 squared?

• 50

• 5

• 625

• 125

Multiple Choice

What number squared is 9?

• 9

• 18

• 3

• 81

Multiple Choice

200

• is a perfect square

• is not a perfect square

Multiple Choice

169

• Is a perfect square.
• Is not a perfect square.

Multiple Choice

Which of the following is a perfect square?

• 39

• 50

• 24

• 81

Multiple Choice

Which of the following is NOT a perfect square?

• 1

• 4

• 100

• 8

Multiple Choice

The √21 is between which two integers?

• 5 and 6

• 20 and 22

• 4 and 5

• 10 and 11

Multiple Choice

The √40 is between which two integers?

• 39 and 41

• 6 and 7

• 5 and 6

• 19 and 21

Multiple Choice

The √40 is between which two integers?

• 39 and 41

• 6 and 7

• 5 and 6

• 19 and 21

Multiple Choice

The √21 is between which two integers?

• 5 and 6

• 20 and 22

• 4 and 5

• 10 and 11

Multiple Choice

What is the area of a square with a side of 7?

• 14
• 28
• 49
• 64

Multiple Choice

In between what two integers is the square root of 44?

• 3 and 4
• 4 and 5
• 5 and 6
• 6 and 7

Multiple Choice

The area of a square is 36 cm².  What is the length of one side?

• 6 cm
• 24 cm
• 9 cm
• 9 cm

Multiple Choice

Square root is the inverse of ____________.

• Cube Roots
• Squaring
• Multiplication
• Absolute Value

Multiple Choice

If you have 196 chairs and you need to arrange them in an equal amount of row and columns, how many chairs will be in each row?

• 12
• 13
• 14
• 15

Multiple Choice

Which of the following is NOT a perfect square?

• 1

• 4

• 100

• 8

Multiple Choice

Which of the following is not a perfect square?

• 110

• 4

• 1

• 81

Multiple Choice

What is the area of a square with a side of 12?

• 144
• 24
• 48
• 6

Multiple Choice

A perfect square is when a whole number is multiplied by itself?

• FALSE
• TRUE

Multiple Choice

To find the square root of a number, you must divide it by 2.

• True
• False

Multiple Choice

12) Which pair of numbers are both between 6 and 7?

Multiple Choice

Between which 2 consecutive numbers on the number line does the square root of 23 lie?

• -5 and -4

• -2 and -1

• 2 and 3

• 4 and 5

Multiple Choice

The area of a square is 117 square meters. Which best represents the length of a side of the square? 

• 10.8 m
• 11 m
• 10 m
• 11.2 m

Multiple Choice

The area of a square is 117 square meters. Which best represents the length of a side of the square?

• 10.8 m

• 11 m

• 10.9 m

• 11.2 m

Multiple Choice

Square roots are the opposite of ____________.

• Cube Roots
• Squaring
• Multiplication
• Absolute Value

Multiple Choice

Evaluate

√36

• 6

• 8

• 18

• -18

Multiple Choice

Find √50. Round your answer to the nearest tenth.

• 7.2

• 6.9

• 7.1

• 7

Multiple Choice

Evaluate √72. Round your answer to the nearest tenth.

• 8.48

• 8.6

• 8.4

• 8.5

Multiple Choice

If I know the area of a square, how do I find the side length?

• I square the area.

• I divide the area by 2.

• I take the square root of the area.

• I divide the area by 4.

Multiple Choice

√100

• 10
• 200
• 5
• 25

Multiple Choice

Which of the following is a perfect square?

• 39
• 50
• 6
• 81

Multiple Choice

Which of the following is NOT a perfect square?

• 1

• 4

• 100

• 8

Multiple Choice

65

• Is a perfect square.
• Is not a perfect square.

Multiple Choice

144

• Is a perfect square.
• Is not a perfect square.

Multiple Choice

What is the square root of 144?

• 4
• 12
• 16
• 32

Multiple Choice

13²

• 26
• 196
• 144
• 169

Multiple Choice

What is the square root of 49?

• 6

• 7

• 8

• 9

Multiple Choice

11²

• 132
• 144
• 121
• 22

Multiple Choice

14²

• 169
• 196
• 28
• 144

Multiple Choice

The √20 is between which two integers?

• 2 & 3
• 3 & 4
• 4 & 5
• 5 & 6

Multiple Choice

The √40 is between which two integers?

• 7 & 8
• 6 & 7
• 5 & 6
• 4 & 5

Multiple Choice

A perfect square is created when a whole number is multiplied by ___

• a different number

• itself

• a two digit number

• a fraction

Multiple Choice

What is 17²?

• 256

• 289

• 324

• 361

​Natural (Counting) Numbers

Natural numbers are also called counting numbers ​because they do not include 0, or negatives. Natural numbers can be counted to infinity and are REAL Numbers.

​

Example : 1,2,3,24,5,6,7,8,9,10,11,12....

Some text here about the topic of discussion

Multiple Choice

What are your counting numbers (1,2,3..)?

• Rational Numbers
• Whole Numbers
• Natural Numbers
• Irrational Numbers

Multiple Choice

The set of counting numbers which is also a subset of real number

= {1, 2, 3, 4, …}

• Rational Number

• Natural Number

• Integer

Whole Numbers

Whole Numbers are a set of natural numbers that start with 0. ​They are apart of the REAL Number set and can be counted into infinity.

​

Examples : 0,1,2,3,4,​5,6,7,8,9,10,11,12....

Some text here about the topic of discussion

Multiple Choice

The set of natural numbers plus a “0”

W = {0, 1, 2, 3,…}

• Natural Numbers

• Integers

• Irrational Numbers

• Whole Numbers

Multiple Choice

True or False: Zero is a counting number.

• True

• False

​Integers

Integers are counting numbers , whole number and negative numbers.

​

• Positive Integer : An integer is positive if it is greater than 0. Ex: 1,2,3...

• Negative Integer : ​An integer is negative if it is less than 0. Ex: -1,-2,-3 ...

• Zero : This number is neither negative nor positive. It is a whole number.

  Ex: -1,-2,-3,-4 0 , 1, 2 ,3,4

Some text here about the topic of discussion

Multiple Choice

The set of natural numbers, their negatives and 0

= {-3, -2, -1, 0, 1, 2, 3,…}

• Whole Numbers

• Integers

• Natural Numbers

Multiple Choice

True or False: Some of the integers are natural numbers.

• True

• False

Rational Numbers

Some text here about the topic of discussion

Multiple Choice

What type of number is $$3.\overline{5}$$  ?

• Integer

• Rational Number

• Irrational Number

• Natural Number

Multiple Choice

True or false: ALL fractions are Rational

• true

• false

Irrational Numbers

Some text here about the topic of discussion

Multiple Choice

Classify the following:
0.04769165821735......

• Irrational
• Rational

Multiple Choice

Which of the following real number categories best matches $$\pi$$     ?

• Rational

• Irrational

• Whole

• Integer

Real Number-ella System

Some text here about the topic of discussion

Multiple Select

Select all sets that the number belongs to:

-6

• Irrational Number

• Rational Number

• Integer

• Whole Number

• Natural Number

Multiple Select

Select all sets that the number belongs to:

0.5

• Irrational Number

• Rational Number

• Integer

• Whole Number

• Natural Number

Multiple Select

Select all sets that the number belongs to:

 $0.\overline{4}$  

• Irrational Number

• Rational Number

• Integer

• Whole Number

• Natural Number

Multiple Select

Select all sets that the number belongs to:

0.32482418....

• Irrational Number

• Rational Number

• Integer

• Whole Number

• Natural Number

Multiple Select

Select all sets that the number belongs to:

 $\sqrt{25}$  

• Irrational Number

• Rational Number

• Integer

• Whole Number

• Natural Number

Multiple Select

Select all sets that the number belongs to:

2

• Irrational Number

• Rational Number

• Integer

• Whole Number

• Natural Number

Multiple Select

Select all sets that the number belongs to:

0

• Irrational Number

• Rational Number

• Integer

• Whole Number

• Natural Number

Multiple Select

Select all sets that the number belongs to:

 $\frac{3}{5}$  

• Irrational Number

• Rational Number

• Integer

• Whole Number

• Natural Number

Multiple Select

Select all sets that the number belongs to:

 $\pi$  

• Irrational Number

• Rational Number

• Integer

• Whole Number

• Natural Number

Multiple Select

Select all sets that the number belongs to:
 $\sqrt{13}$  

• Irrational Number

• Rational Number

• Integer

• Whole Number

• Natural Number

Multiple Select

Select all sets that the number belongs to:
 $\frac{2}{3}$  

• Irrational Number

• Rational Number

• Integer

• Whole Number

• Natural Number

Multiple Select

Select all sets that the number belongs to:
 $\frac{-10}{2}$  

• Irrational Number

• Rational Number

• Integer

• Whole Number

• Natural Number

Multiple Select

Select all sets that the number belongs to:

4.00

• Irrational Number

• Rational Number

• Integer

• Whole Number

• Natural Number

Multiple Select

Select all sets that the number belongs to:

 $-\sqrt{25}$  

• Irrational Number

• Rational Number

• Integer

• Whole Number

• Natural Number

Multiple Select

Select all sets that the number belongs to:

 $1.\overline{12}$  

• Irrational Number

• Rational Number

• Integer

• Whole Number

• Natural Number

Multiple Select

Select all sets that the number belongs to:

 $\left|-10\right|$  

• Irrational Number

• Rational Number

• Integer

• Whole Number

• Natural Number

Multiple Select

Select all sets that the number belongs to:
 $\sqrt{3}$  

• Irrational Number

• Rational Number

• Integer

• Whole Number

• Natural Number

Multiple Select

Select all sets that the number belongs to:
 $6^0$  

• Irrational Number

• Rational Number

• Integer

• Whole Number

• Natural Number

Multiple Select

Select all sets that the number belongs to:
 $\frac{12}{4}$  

• Irrational Number

• Rational Number

• Integer

• Whole Number

• Natural Number

Multiple Select

Select all sets that the number belongs to:
 $\frac{4}{3}$  

• Irrational Number

• Rational Number

• Integer

• Whole Number

• Natural Number

Multiple Choice

Classify the number 3

• Natural, Whole, Integer, Rational
• Whole, Rational
• Integer
• Rational

Multiple Choice

Classify the number 0

• Whole
• Integer
• Rational
• All of the above

Multiple Choice

-14 could NOT be which type of number?

• Integer
• Real
• Rational
• Natural

Multiple Choice

Classify 17/10

• Whole
• Rational
• Natural
• None of the above

Multiple Choice

What number below is a natural, whole, integer, rational, and real number ?

• -4
• 5.1
• 0.7
• 3

Multiple Choice

Classify 0

• Whole
• Integer
• Rational
• All of the above

Multiple Choice

Classify the following:
 -78

• integer
• integer, real
• integer, whole, rational
• integer, rational, real

Multiple Choice

How would 5/9 be classified?

• rational and real
• whole and integer
• only real
• only irrational

Multiple Choice

Explain the error(s).

• -1.2 isn't an integer.
• -2 isn't a whole number and 3.4 isn't a rational number.
• -2 isn't a whole number and -1.2 isn't an integer.
• The numbers are graphed correctly.

Multiple Choice

What type of number is  ⅛

• whole 
• rational
• irrational
• integers

Similar Triangles

Multiple Choice

A triangle has angle measurements of 26°, 59°, and 95°. What kind of triangle is it?

• acute triangle
• right triangle
• obtuse triangle
• none of the above

Multiple Choice

A triangle has side lengths of 19 centimetres, 19 centimetres, and 20 centimetres. What type of triangle is this?

• equilateral triangle

• isosceles triangle

• scalene triangle

• none of the above

Multiple Choice

When classifying a triangle by its sides, what type of triangle has exactly two equal sides?

• equilateral triangle

• isosceles triangle

• scalene triangle

• none of the above

Multiple Choice

In a triangle, what is the sum of the interior angles?

• 100%

• 180 degrees

• it varies

• 360 degrees

Multiple Choice

Find the measure of the indicated angle. 

• 95
• 85
• 35
• 45

Multiple Choice

Find the measure of the indicated angle. 

• 26
• 36
• 85
• 144

Multiple Choice

Find the missing angle.

• 29° 
• 39° 
• 49° 
• 59° 

Multiple Choice

Which would be the best classification for the triangle shown?

• acute isosceles
• right scalene
• acute scalene
• obtuse scalene

Multiple Choice

Which would be the best classification for the triangle shown?

• right isosceles
• obtuse scalene
• obtuse isosceles
• right scalene

Multiple Choice

What is the value of x?

• 60
• 5
• 10
• -3

Multiple Choice

What is the measure of angle A?

• 30

• 45

• 47

• 50

Multiple Choice

Triangle DEF has a missing angle measure. If the m∠E is 93 degrees and the m∠F is 24 degrees. What is the measure of angle D?

• 63

• 36

• 90

• 76

Multiple Choice

Triangle DEF. If the m∠E is 60 degrees and the m∠F is 60 degrees. What type of triangle is this?

• acute, isosceles

• obtuse, isosceles

• acute, equilateral

• acute, scalene

Special Right Triangles

​

Multiple Choice

Find the missing side lengths.

• a = 4, b = 4
• a = 4, b = 2√2
• a = 2√2,  b = 4
• a = 4, b = 4

Multiple Choice

What is the length of x in this 45-45-90 triangle?

• 4√2
• 4
• 8
• 4√3

Multiple Choice

What is the length of u and v in this 30-60-90 triangle?

• u = 8 v = 4√3
• u = 4√2 v = 8
• u = 16 v = 8
• u = 4√3 v = 8

Multiple Choice

Find a.

• 3

• $3\sqrt{3}$

• 6

• $\sqrt{3}$

Multiple Choice

Find x.

• 10

• $10\sqrt{3}$

• $10\sqrt{2}$

• 20

Multiple Choice

Which side is the long leg in this 30-60-90 triangle? (not the hypotenuse)

• 4
• u
• v

Special Right Triangles

​

Multiple Choice

Find the missing side lengths.

• a = 4, b = 4
• a = 4, b = 2√2
• a = 2√2,  b = 4
• a = 4, b = 4

Multiple Choice

What is the length of x in this 45-45-90 triangle?

• 4√2
• 4
• 8
• 4√3

Multiple Choice

What is the length of u and v in this 30-60-90 triangle?

• u = 8 v = 4√3
• u = 4√2 v = 8
• u = 16 v = 8
• u = 4√3 v = 8

Multiple Choice

Find a.

• 3

• $3\sqrt{3}$

• 6

• $\sqrt{3}$

Multiple Choice

Find x.

• 10

• $10\sqrt{3}$

• $10\sqrt{2}$

• 20

Multiple Choice

Which side is the long leg in this 30-60-90 triangle? (not the hypotenuse)

• 4
• u
• v

Multiple Choice

Which would be the best classification for the triangle shown?

• acute isosceles
• right scalene
• acute scalene
• obtuse scalene

Multiple Choice

Which would be the best classification for the triangle shown?

• acute isosceles
• equiangular scalene
• equiangular isosceles
• equiangular equilateral

Multiple Choice

Which would be the best classification for the triangle shown?

• acute isosceles
• obtuse scalene
• obtuse isosceles
• acute scalene

Multiple Choice

Which would be the best classification for the triangle shown?

• right isosceles
• obtuse scalene
• obtuse isosceles
• right scalene

Multiple Choice

Which would be the best classification for the triangle shown?

• right isosceles
• obtuse scalene
• obtuse isosceles
• acute scalene

Multiple Choice

What is the value of the missing angle?

• 61
• 50
• 60
• 69

Multiple Choice

What is the value of x?

• 60
• 5
• 10
• -3

Multiple Choice

What is the value of x?

• 10
• 5
• -12
• 9

Multiple Choice

What is the value of x?

• 64
• 46
• 127
• 38

Multiple Choice

What is the value of x?

• 75
• 80
• 63
• 60

Multiple Choice

What is the value of the ANGLE A (not just x)?

• 151
• 68
• 151
• 70

Multiple Choice

What is the value of x?

• 30
• 45
• 47
• 50

Multiple Choice

Which angle is the vertex angle?

• <C
• <A
• <B

Multiple Choice

Which segment is the base?

• Segment AB
• Segment BC
• Segment AC

Multiple Choice

What is the value of x?

• 51
• 49
• 78

Multiple Choice

What is the measure of angle 2?

• 50
• 65
• 115

Multiple Choice

The triangles shown are similar. Which side corresponds with side BC?

• AB

• DE

• EF

• CA

Multiple Choice

The triangles shown are similar. Which angle corresponds to angle D?

•  $\angle$  A

•  $\angle$  B

•  $\angle$  C

•  $\angle$  E

Multiple Choice

The triangles shown are similar. What is the scale factor from ABC to DEF?

• 2

• 3

• 4

• 5

Multiple Choice

The triangles shown are similar. Find the length of side EF.

• 3

• 12

• 15

• 18

Multiple Choice

All the angles in a triangle

add up to ....

• 90 degrees

• 180 degrees

• 360 degrees

• It depends on the triangle

Multiple Choice

Find the missing angle in the triangle.

• $81^o$

• $91^o$

• $99^o$

• $101^o$

Multiple Choice

Can angles measuring 78^o, 30^o, and 82^o make a triangle?

• Yes

• No

Multiple Choice

If two side lengths of a triangle are 30 cm and 50 cm, what is a possible length of the third side?

• 70 cm

• 80 cm

• 100 cm

Multiple Choice

Find the measure of angle x.

• 125^o

• 45^o

• 60^o

• 35^o

Multiple Choice

A triangle with all 3 angles measuring less than 90^o is called a(n) ...

• Acute Triangle

• Right Triangle

• Obtuse Triangle

Multiple Choice

Can the side lengths of 3 ft, 7 ft, and 9 ft create a triangle? Explain.

• No, the shape won't close.

• Yes, the two shorter sides add up to be larger than the third side.

• There is not enough information.

Multiple Choice

A triangle with two congruent sides

(two sides that are the same length)

is called a(n) ...

• Isosceles Triangle

• Scalene Triangle

• Equilateral Triangle

• None of the Above

Multiple Choice

A triangle with no congruent sides

is called a(n) ...

• Isosceles Triangle

• Scalene Triangle

• Equilateral Triangle

• None of the Above

Multiple Choice

A triangle with one angle

greater than 90^o is called a(n) ...

• Acute Triangle

• Right Triangle

• Obtuse Triangle

Multiple Choice

The triangles are similar. Angle B is 40^o.

What is the measure of angle E?

• 130^o

• 50^o

• 40^o

• None of the Above

Multiple Select

Select ALL the true facts

about triangles.

• Their angle measures add up to 180^o.

• Corresponding angles in similar triangles change with a scale factor.

• The sum of the two shortest sides in a triangle must be larger than the third side.

• Triangles are not polygons.

Multiple Choice

Triangle ABC and triangle FDE are ...

• Similar

• Congruent

• Different Sizes

• Right Triangles

Multiple Choice

Find the area of the triangle. Remember: 

 $A=\frac{1}{2}\times b\times h$  

• 10  $cm^2$  

• 13  $cm^2$  

• 20 $cm^2$  

• 40  $cm^2$  

Multiple Choice

Find the area of the triangle. Remember: 

$A=\frac{1}{2}\times b\times h$

• 54 $cm^2$

• 108 $cm^2$

• 27 $cm^2$

• 12 $cm^2$

Multiple Choice

**CHALLENGE**

Find the missing angles.

• x=50^o, y=63^o, z=32^o

• x=50^o, y=63^o, z=63^o

• x=67^o, y=63^o, z=42^o

• x=67^o, y=63^o, z=32^o

Pythagorean Theorem

​

The Sides of a Triangle

The shorter sides of the triangle are always the legs.

The longest length of a triangle is always the hypotenuse.

Multiple Choice

The Pythagorean Theorem ONLY works on which triangle? 

• obtuse
• scalene
• isosceles
• right

Multiple Choice

Side c on a right triangle is ALWAYS the longest.

• true

• false

Multiple Choice

Which side is the hypotenuse?

• 9

• x

• 14

Multiple Choice

Which sides are the legs of the triangle?

• 9 and 15

• 9 and 12

• 12 and 15

• 15

How to Solve

1. Determine what side is missing.

2. Plug in what you know into the equation.

3. Simplify the equation.

4. Solve for the missing side.

5. If needed round to the nearest tenth!

Multiple Choice

Which equation can be used to solve for "x"?

• 15² – x² = 21²

• x² – 15² = 21²

• 15² + 21² = x²

• 21² – 15² = x²

Multiple Choice

Determine the length of the missing side.

• 7

• 8

• 17

• 23

Multiple Choice

_{^{Find the missing side}}

• 9
• 41
• 6.4
• 3

Multiple Choice

Find h

• 35.60
• 35.00
• 35.71
• 61.03

Multiple Choice

Find the value of x.

• 7
• 8
• 9
• 10

Multiple Choice

solve for c

• 7
• 9
• 4
• 13

Word Problems

When solving word problems, it helps to draw a triangle and fill in the missing information.

Multiple Choice

Lisa drives her car 46 km south and then 13 km east. How far is she from her starting point?

• 44.1 km

• 59 km

• 47.8 km

• 33 km

Multiple Choice

A baseball "diamond" is actually a square with sides of 90 feet. If a runner tries to steal second base, how far must the catcher, at home plate, throw to get the runner "out"? (Distance across the diagonal)

• 180 feet

• 90 feet

• 13.4 feet

• 127.3 feet

Multiple Choice

The slide at the playground has a height of 6 feet. The base of the slide measured on the ground is 8 feet. What is the length of the slide?

• 8 feet

• 5.29 feet

• 10 feet

• 14 feet

Poll

How do you feel about applying and using the Pythagorean theorem?

• I am lost

• I think I get it

• I got it

• EASY PEASY

Labelling

Drag the correct letter to the box.

Drag labels to their correct position on the image

B

A

C

Dropdown

The ​

Select answer

of the ​

Select answer

created by the legs of a ​

Select answer

triangle are ​

Select answer

to the area of the ​ square created by the ​

Select answer

.

Multiple Choice

Which set of side lengths would form a right triangle?

• 6, 9, 12

• 8, 10, 12

• 9, 40, 41

• 5, 10, 12

Multiple Choice

A rectangular high jump pit is 25 feet long and 10 feet wide. Which of these is closest to the diagonal distance across the pit?

• 25 feet

• 26 feet

• 27 feet

• 28 feet

Multiple Choice

Which equation will help you find the missing side?

• $$4^2+10^2=c^2$$

• $$10^2-4^2=c^2$$

• $$c^2=100+10^2$$

• $$c^2+4^2=10^2$$

Multiple Choice

Which of these is closest to the length of PQ?

• 10.9 units

• 13 units

• 2.4 units

• 169 units

Multiple Choice

Please read the question carefully:

• A
• B
• C
• D

Multiple Choice

Please read the question carefully:

• A
• B
• C
• D

Multiple Choice

 Find the distance between these 2 points.

• 5.8
•  6.3
• 8.1
• 40

Multiple Choice

A rectangular pool at Andy's gym measures 25 m by 50 m. How far would Andy swim if he swims across the pool diagonally?

• 5 m

• 8.7 m

• 43.3 m

• 55.9 m

Multiple Choice

Level 1

The Pythagorean Theorem ONLY works on which triangle?

• obtuse

• scalene

• isosceles

• right

Multiple Choice

Level 1

If a right triangle has side lengths 6, 6.7 and 3, which side is the hypotenuse?

• 6

• 6.7

• 3

• 15.7

• None of them

Multiple Choice

Level 2

Solve for the value of y

• 13

• 5

• 23

• 10

Multiple Choice

Level 3

Find the length of the missing side.

• 20 in.

• 68 in.

• 16 in.

• 80 in.

Multiple Choice

Level 4

Solve for x.

• 38.9

• 40.2

• 45.6

• 54

Multiple Choice

An airplane flies 56 miles due north and then 33 miles due east. How many miles is the plane from its starting point?

• 65 miles
• 89 miles
• 45.4 miles
• We don't have enough information.

Multiple Choice

A piece of paper that Brittany has is 11 inches tall and 8 inches wide. She draws a straight line diagonally across the paper. How long is the line she drew?

• 7.5 in
• 12.4 in
• 13.6 in 
• 14.3 in

Multiple Choice

In a right triangle, if a = 8 and c = 17, what is the correct setup to find the value of b?

• $17^2+8^2=b^2$

• $8^2+b^2=17^2$

• $17^2+b^2=8^2$

• $\frac{8^2}{b^2}=\frac{17^2}{100}$

Multiple Choice

The longest side of a right triangle is DIRECTLY ACROSS from the...

• right angle.
• acute angle.
• obtuse angle.

Multiple Choice

What is the final step in solving this work for c?
a² + b² = c²
3² + 4² = c²
9 + 16 = c²
25 = c²

• Divide both sides by 2
• Take the square root of both sides

Multiple Choice

The slide at the playground has a height of 6 feet. The base of the slide measured on the ground is 8 feet. What is the length of the slide?

• 8 feet

• 5.29 feet

• 10 feet

• 14 feet

Multiple Choice

The bottom of a 13-foot straight ladder is set into the ground 5 feet away from a wall. When the top of the ladder is leaned against the wall, what is the distance above the ground it will reach?

• 12 feet

• 13.9 feet

Multiple Choice

A baseball "diamond" is actually a square with sides of 90 feet. If a runner tries to steal second base, how far must the catcher, at home plate, throw to get the runner "out"? (Distance across the diagonal)

• 180 feet

• 90 feet

• 13.4 feet

• 127.3 feet

Multiple Choice

During a football play, Odell Beckham Jr. runs a straight route 40 yards up the sideline before turning around and catching a pass thrown by Eli Manning. On the opposing team, a defender who started 20 yards across the field from Beckham saw the play setup and ran a slant towards Beckham. What was the distance the defender had to run to get to the spot where Beckham caught the ball?

• 34.6 yards

• 44.7 yards

• 60 yards

• 40 yards

Multiple Choice

How far from the base of a house do you need to place a 15' ladder so that is exactly reaches the top of a 12' wall?

• 9 feet

• 19.2 feet

• 81 feet

• 369 feet

Distance Formula

Review and Practice

Multiple Choice

Which of the following represents the Distance Formula?

• $a^2\ +\ b^2\ =\ c^2$

• $d\ =\ \sqrt{\left(x_{2\ }-\ x_1\right)^2\ +\ \left(y_{2\ }-\ y_1\right)^2}$

Multiple Select

Which of the following shows the correct way to insert the following coordinates into the DIstance Formula?

(3, 4) , (7, 1)

• $d\ =\ \sqrt{\left(4\ -\ 3\right)^2\ +\ \left(7\ -\ 1\right)2}$

• $d\ =\ \sqrt{\left(7\ -\ 3\right)^2\ +\ \left(1\ -\ 4\right)^2}$

• $d\ =\ \sqrt{\left(7\ -\ 4\right)^2\ +\ \left(1\ -\ 3\right)^2}$

• $d\ =\ \sqrt{\left(3\ -\ 7\right)^2\ +\ \left(4\ -\ 1\right)^2}$

• $d\ =\ \sqrt{\left(3\ +\ 7\right)^2\ -\ \left(4\ +\ 1\right)^2}$

Multiple Choice

Find the distance between the points (5, 7) and (-2, -2).

• 5.7

• 5.8

• 8.6

• 11.4

Multiple Choice

What is the distance between (-3, 2) and (5, -1)

• 11

• 8.5

• 1.7

• 7.3

Multiple Choice

Find the distance between (0, 10) and (12, 1).

• 12

• 11

• 15

• 16

Pythagorean Theorem Review

Multiple Choice

One end of a cable is attached to the top of a flag pole and the other end is attached 6 feet away from the base of the pole. The height of the flagpole is 12 feet. What is length of the cable?

• 13.4 ft

• 13.1 ft

• 6 ft

• 10.4 ft

Multiple Choice

Rectangle JKLM is shown. To the nearest tenth, what is the distance from J to L?

• 5.0 cm

• 10.2 cm

• 15.3 cm

• 21.0 cm

Multiple Choice

If a triangle has sides 13, 17, and 27 is it right, acute or obtuse?

• Right

• Acute

• Obtuse

Multiple Choice

Is a triangle with sides 21, 24 and 28 right, acute or obtuse?

• Right

• Acute

• Obtuse

Multiple Choice

Is a triangle with sides 7, 24, and 25 right, acute, or obtuse?

• Right

• Acute

• Obtuse

Multiple Choice

To the nearest tenth, find the hypotenuse of a right triangle with legs 12.1 and 16.2.

• 408.9

• 116.0

• 20.2

• 10.8

Multiple Choice

If a triangle has sides 13, 17, and 27 is it right, acute or obtuse?

• Right

• Acute

• Obtuse

Multiple Choice

Which letter matches the coordinate (4, -6)?

• G
• Z
• K
• None of the above

Multiple Choice

On the coordinate plane, which line is the y-axis?

• Horizontal Line (Side to Side)
• Vertical Line (Up and Down)

Multiple Choice

What letter is at (7, -6)?

• D
• L
• X
• There is no letter at those coordinates.

Multiple Choice

Find the direct distance between the court house and the town hall.

• 26
• 6.8
• 10
• 7.2 km

Multiple Choice

What is the distance between the two points?

• 6.3
• 6.5
• 6.7
• 16

Multiple Choice

Find the distance.

• 7.1
• 7.8
• 8.7
• 8.9

Multiple Choice

Becky leaves school to go home. She walks 6 blocks North and then 8 blocks west. How far is Becky from the school?

• 14 blocks

• 12 blocks

• 10 blocks

• 8.5 blocks

Multiple Choice

Find the length of the missing side. 

• 17 cm
• 22 cm
• 15 cm
• 13 cm

Multiple Choice

Find the distance between ( 1, 3) and (5, 6) 

• 3
• 4
• 5
• 6

Multiple Choice

Determine if the following lengths will make a right triangle:
12, 5, 7

• Yes 
• No

Multiple Choice

What is the opposite of squaring a number?

• divide
• multiply 
• fractions
• square root

Multiple Choice

Find the distance between (3, 24) and (7, 56).

• 32.1
• 32.2
• 32.3
• 32.4

Multiple Choice

What is the distance between (2,9) and (1,5)?

• 15
• 17
• 4.12
• 3.87

Multiple Choice

If you were to plot the point (4, -12) what would be the correct method?

• Up 4, left 12
• Right 4, up 12
• Down 4, left 12
• Right 4, down 12

Multiple Choice

Estimate √28

• 6 3/11

• 5 3/8

• 5 3/11

Multiple Choice

Find the direct distance between the library and the town hall.

• 26

• 6

• 10

• 3

Multiple Choice

What is the distance between AB

• 0

• 8

• 9

• 7

Multiple Choice

What is the distance between AB?

• 0

• undefined

• 5

• 4

Multiple Choice

The distance formula is another way to write which of the following?

• quadratic formula

• slope formula

• Pythagorean theorem

• none of these answers

Multiple Choice

How is the distance formula correctly written:

• $$d\ =\ \sqrt{\left(y_{1\ }-\ y_2\right)^2\ -\left(x_{2\ }-\ x_1\right)^2}\$$

• $$d\ =\ \sqrt{\left(x_{2\ }-\ x_1\right)^2\ +\ \left(y_{2_{\ }}-\ y_1\ \right)^2}$$

• $$d\ =\ \sqrt{\left(y_{1\ }-\ y_2\right)^2\ +\ \left(x_{2\ }-\ x_1\right)^2}$$

• d = $$\sqrt{\left(x\right)^2-\ \left(y\right)^2}$$

Multiple Choice

A(3,1) B(-2,-1) written correctly is:

• $$\sqrt{\left(-2-3\right)^2\ +\ \left(-1-1\right)^2}$$

• $$\sqrt{\left(1-3\right)^2\ +\ \left(-1-2\right)^2}$$

• $$\sqrt{\left(-2-3\right)^2\ -\ \left(-1-1\right)^2}$$

• $$\sqrt{\left(-2-3\right)^2\ -\ \left(-1-1\right)^2}$$

Multiple Choice

How is AB written in the distance formula?

• 
  $$d\ =\ \sqrt{\left(5-3\right)^2\ +\ \left(0--2\right)^2}$$
  

• $$d\ =\ \sqrt{\left(2-5\right)^2\ +\ \left(3\ -0\right)^2}$$

• $$d\ =\ \sqrt{\left(5-3\right)^2\ -\ \left(0--2\right)^2}$$

• $$d\ =\ \sqrt{\left(4-3\right)^2\ -\ \left(2-4\right)^2}$$

Multiple Choice

Find the distance.

• 9.7
• 10.7
• 11.7
• 12.7

Multiple Choice

What is the distance between (2,9) and (1,5)?

• 15
• 17
• 4.12
• 3.87

Multiple Choice

Find the distance between (-4, 5) and (7, 18).

• 15.96
• 16.08
• 16.23
• 17.03

Multiple Choice

Find the direct distance between the court house and the town hall.

• 26
• 6.8
• 10
• 7.2 km

Multiple Choice

What is the length of y in this picture?

• 45
• 5√2
• 90
• 5

Multiple Choice

What is the length of x in this 45-45-90 triangle?

• 4√2
• 4
• 8
• 4√3

Multiple Choice

In this isosceles triangle, what is the length of x?

• 8√2

• $\frac{8}{\sqrt{2}}$

• 16

• 8

Multiple Choice

Which is the length of v in this 30-60-90 triangle?

• $4\sqrt{3}$

• 4

• 8

• $4\sqrt{2}$

Multiple Choice

What is the length of the short leg of this 30-60-90 triangle?

• 6

• $\frac{6}{\sqrt{3}}$

• 3

• $\frac{6}{\sqrt{2}}$

Multiple Choice

In this 30-60-90 triangle, what is the length of the hypotenuse?

• 4√2

• 4√3

• 4

• 8

Multiple Choice

In this 30-60-90 triangle, what is the length of the long leg?

• 6√2

• 3√3

• 12

• 6√3

Multiple Choice

What is x in this 30-60-90 triangle?

• x = 6

• x = 3√2

• x = 3√3

• x = 3√3

Multiple Choice

What is a in this 30-60-90 triangle?

• a = 7√3

• a = 7√2

• a = 14

• a = 14√3

Multiple Choice

Find x.

• 10
• 10√3
• 10√2
• 20

Multiple Choice

Find x.

• 22
• 11√3
• 11√2
• 11

Multiple Choice

Find a.

• 12
• 24
• 24√3
• 16

Multiple Choice

Find the value of y.

• 8
• 4
• 2√3
• 8√3

Multiple Choice

What is the length of x in this picture?

• 45

• 5√2

• 90

• 5

Multiple Choice

What is the length of y in this 45-45-90 triangle?

• 4√2

• 4

• 8

• 4√3

Multiple Choice

What is y in this 30-60-90 triangle?

• $y=6$

• $y=3\sqrt{2}$

• $y=3\sqrt{3}$

• $y=\frac{3}{\sqrt{3}}$

Multiple Choice

What is b in this 30-60-90 triangle?

• b=3.5√3

• b = 3.5

• b = 7

• b = 7√3

Multiple Choice

What is the measure of side b?

• 5

• 10√2

• $\frac{10}{\sqrt{2}}$

• 10√3

Multiple Choice

What is the length of x in this triangle?

• 14

• $7\sqrt{3}$

• 3.5

• $\frac{14}{\sqrt{3}}$

Multiple Choice

What is the length of y in this triangle?

• 14

• $7\sqrt{3}$

• 3.5

• $\frac{7}{\sqrt{3}}$

Multiple Choice

Which trigonometric ratio should you use?

• Tangent Ratio

• Sine Ratio

• Cosine Ratio

• Any ratio

Multiple Choice

 Find side AB?

• 20 m
• 5 m
• 11.54 m
• 8.66 m

Multiple Choice

Choose the correct ratio.

• A
• B
• C
• D

Multiple Choice

Find the length of side w.

• 21.4 cm
• 18.0 cm
• 36.5 cm
• 43.6 cm

Multiple Choice

Find the measure of the indicated angle (?) round to the nearest tenth.

• 9.4
• 55.2
• 20.15
• 19.4

Multiple Choice

Solve for the misssing distance

• 18.9
• 19.5
• 47
• 27.5

Multiple Choice

Which scenario describes the picture shown?

• A 5 foot ramp is 8 feet away from a building.  What is the angle that the ramp makes with the ground?
• A 5 foot ramp leans against an 8 foot structure.  What is the angle that the ramp makes with the ground?
• An 8 foot ramp leans
  against a building 5 feet away.  What angle does the ramp make with the ground?
• A 5 foot man is 8 feet away from a building.  What is the angle of elevation?

Multiple Choice

Solve for the missing angle.

• 50.5 degrees
• 12.7 degrees
• 36.9 degrees
• 72.2 degrees

Multiple Choice

Solve for the triangle:

• AB = 14 , < A = 48.59, <B = 41.41
• AB = 10 , <A = 36.87 , <B= 53. 13
• AB = 10, <A = 53.13 , <B=36.87

Multiple Choice

Find the exact value of x. 

• √29
• √7
• 7
• 10

Multiple Choice

When the sun is 62 degrees above the horizon, a building cast a shadow 18 meters long. How tall is the building?

• 34 m

• 16 m

• 9 m

• 11 m

Multiple Choice

Dustin is stuck at the top of a Ferris wheel. His mother is standing 38 feet from the base of the wheel watching him. If the angle of elevation from Dustin's mom to Dustin is 73^o, how far off the ground is Dustin? 

• 118.2 ft
• 120.9 ft
• 124.3 ft
• 126.5 ft

Multiple Choice

A sailing boat, which was supposed to be travelling north, veered off course and travelled N 45° E for a distance of 0.64 km, as shown. How far east had the sailing boat travelled? Give your answer to 2 decimal places.

• 0.45 km
• 1.28 km
• 0.64 km
• 1.09 km

Multiple Choice

A kite is on a 300-ft string. The angle of elevation from the ground to the kite is 39°. Which is the best estimate of the height of the kite above the ground? 

• 629 feet
• 243 feet
• 189 feet
• 233 feet

Multiple Choice

What is the length of x in this 45-45-90 triangle?

• 4√2
• 4
• 8
• 4√3

Multiple Choice

What is the length of u and v in this 30-60-90 triangle?

• u = 8 v = 4√3
• u = 4√2 v = 8
• u = 16 v = 8
• u = 4√3 v = 8

Multiple Choice

You are making a guitar pick that resembles an equilateral triangle with side lengths of 32 millimeters. What is the approximate height of the pick? (hint: use 30-60-90 theorems)

• 32√3
• 16√3
• 32
• 16√2

Multiple Choice

What if the value of x?

• 16
• 12
• 4
• 64

Multiple Choice

Find the value of x.

• 15√5

• 5√5

• 5√3

• 3√5

Multiple Choice

Find the value of x.

• 2√7

• 7√2

• √28

• 28

Multiple Choice

If you are given the two sides that are not the hypotenuse, which trig function should you use?

• sine
• cosine
• tangent
• cotangent

Multiple Choice

Which one is the easy way to remember trigonometric ratios?

• Sah Coh Toa
• Soh Cah Toa
• Soh Cah Tao
• Soh Ceh Toa

Multiple Choice

Choose the correct ratio.

• cos(33)=x/14
• sin(33)=x/14
• cos(33)=14/x
• sin(33)=14/x

Multiple Choice

Solve for x. Round to the nearest tenth.

• 103.5
• 4.7
• 55.0
• 23.4

Multiple Choice

Solve for x. Round to the nearest tenth.

• 9.8
• 0.1
• 0.038
• 9.9

Multiple Choice

What is the correct equation to solve for x ?

• tan( 46 ) = 17/x
• sin ( 46 ) = x/17
• tan (46 ) = x/17
• cos (46) = x/17

Multiple Choice

• A
• B
• C
• D

Multiple Choice

What equation can be used to solve for x?

• Sin(40°)= x/40

• Sin(40º)=x/19

• Cos(40º)=x/19

• Tan(40°)=19/x

Multiple Choice

Solve for x.

• 10
• 11.3
• 12.0
• 15.0

Multiple Choice

Solve for x.

• 50.7
• 50.1
• 60.7
• 61.0

Multiple Choice

Which triangle is correctly labeled?

Multiple Choice

Solve for x. Round to the nearest tenth.

• 7.5

• 34.1

• 14.1

• 30.1

Multiple Choice

Find the length of side w.

• 21.4 cm

• 18.0 cm

• 36.5 cm

• 43.6 cm

Multiple Choice

Find the length of the missing side x...

Round your answer to 1 decimal place.

• 3.8 cm

• 28.8 cm

• 3.9 cm

• 3.6 cm

Multiple Choice

Solve for the misssing distance

• 18.9
• 19.5
• 47
• 27.5

Multiple Choice

Susan is flying a kite, which gets caught in the top of a tree.  Use the diagram to estimate the height of the tree. 

• 63 ft
• 65 ft
• 74 ft
• 87 ft

Multiple Choice

Find the length of the missing side x...

Round your answer to 1 decimal place.

• 10.3 cm

• 10.2 cm

• 17.5 cm

• 8.6 cm

Multiple Choice

If you are given the hypotenuse and an adjacent side, which trig function should you use?

• sine
• cosine
• tangent
• cotangent

Multiple Choice

Which trigonometric ratio is correct?

• sinA= opp/adj
• cosA= opp/hyp
• tanA= opp/adj
• sinA= adj/opp

Multiple Choice

Which is the correct set up to solve for x?

• cos 55 = x / 29
• sin 55 = 29 / x
• tan 55 = 29 / x
• cos 29 = x / 55

Multiple Choice

What is the correct ratio?

• 7/24
• 24/7
• 7/25
• 24/25

Multiple Choice

What is the correct ratio?

• 3/5
• 3/4
• 4/5
• 4/3

Multiple Choice

What is the ratio of sin D?

• 4/5
• 3/5
• 5/4 
• 5/3

Multiple Choice

Find the measure of the indicated angle (?) round to the nearest tenth.

• 9.4
• 55.2
• 20.15
• 19.4

Multiple Choice

Find the length of side w.

• 21.4 cm
• 18.0 cm
• 36.5 cm
• 43.6 cm

Multiple Choice

Solve for x.

• 50.7
• 50.1
• 60.7
• 61.0

Multiple Choice

Solve for the missing angle.

• 50.5 degrees
• 12.7 degrees
• 36.9 degrees
• 72.2 degrees

Multiple Choice

Solve for the missing distance. This is a right triangle.

• 18.9

• 19.5

• 47

• 27.5

Multiple Choice

Find side AB? This is a right triangle.

• 20 m

• 5 m

• 11.54 m

• 8.66 m

Multiple Choice

m∠A = ?

• 36.9⁰
• 38.7⁰
• 53.1⁰
• 30.1⁰

Multiple Choice

What would be used to find the distance across the lake?

• Quadratic Formula
• Law of Cosines
• Law of Sines
• Trigonometric Ratios

Multiple Choice

What is the distance across the lake to the nearest yard?

• 275 yd
• 315 yd
• 422 yd
• 296 yd

Multiple Choice

What would be used to find the distance from the Ranger's Tower to the fire?

• Quadratic Formula
• Law of Cosines
• Law of Sines
• Trigonometric Ratios

Multiple Choice

What is the distance from the Ranger's Tower to the fire?

• 84.5 ft
• 266.2 ft
• 202.4 ft
• 235.9 ft

Multiple Choice

What is length x to the nearest tenth? 

• 10.7
• 21.9
• 39.8
• 113.9

Multiple Choice

What is the measure of angle A?

• 50 degrees
• 60 degrees
• 78 degrees
• 74 degrees

Multiple Choice

Find a.

• 3
• 3√3
• 6
• 2√3

Multiple Choice

Find b.

• 12

• 9√3

• 6

• 6√3

Multiple Choice

What is the value of x?

• 12√2

• 2√12

• 24

• 12√3

Multiple Choice

• A
• B
• C
• D

Multiple Choice

What type of triangle do the lengths 20, 23, and 15 form?

• right

• acute

• obtuse

• not a triangle

Multiple Choice

What type of triangle do the lengths 35, 19, and 12 form?

• right

• acute

• obtuse

• not a triangle