untitled

Multiple Choice

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

• 14 blocks
• 12 blocks
• 10 blocks
• 8.5 blocks

Multiple Choice

The Pythagorean Theorem ONLY works on which triangle? 

• obtuse
• scalene
• isosceles
• right

Multiple Choice

Find the length of the missing side. 

• 17 cm
• 22 cm
• 15 cm
• 13 cm

Multiple Choice

Is this a right triangle?

• Yes

• No

Multiple Choice

solve for c

• 7
• 9
• 4
• 13

Multiple Choice

What is the hypotenuse (c)?

• the two sides that make up the right angle
• the longest side, across from the right angle
• the shortest side
• the straight side of the triangle

Multiple Choice

Casey travels from her house directly west to the bank and then directly north from the bank to the mall. She then travels home on the road connecting the mall and her house. What is her total distance traveled?

• 17 miles
• 32 miles
• 37 miles
• 40 miles

Multiple Choice

Find the value of the unknown side.

• 10 cm

• 13 cm

• 12 cm

• 5 cm

Multiple Choice

Find the value of x.

• 24 cm

• 13 cm

• 12 cm

• 21 cm

Multiple Choice

Find the value of x.

• 3

• 6.40

• 1.71

• 1.5

Multiple Choice

Find the distance of the wall to the ladder.

• 5

• 7

• 9

• 11

Multiple Choice

Find the value of x.

• 8 cm

• 5 cm

• 7 cm

• 9 cm

Multiple Choice

Which expression can be used to find h, the distance from the top of the ladder to the bottom of the building?

• $$50^2+35^2$$

• $$\sqrt{50^2+35^2}$$

• $$\sqrt{50^2-35^2}$$

• $$50^2-35^2$$

Multiple Choice

Which expression can be used to find the length of the missing side?

• $$12^2+5^2$$

• $$12^2-5^2$$

• $$\sqrt{12^2-5^2}$$

• $$\sqrt{12^2+5^2}$$

Multiple Choice

Which expression can be used to find the length of the missing side?

• $$\sqrt{82^2+18^2}$$  

• $$\sqrt{82+18}$$  

• $$\sqrt{82-18}$$  

• $$\sqrt{82^2-18^2}$$  

​C is always across from the 90 degree angle.

Side a and b are called legs.

Pythagorean triples - 3 whole numbers that satisfy the Pythagorean Theorem.

​

Examples:

​(3, 4, 5), (5, 12, 13), (8, 15, 17), (7, 24, 25) , (20, 21, 29) , (12, 35, 37), (9, 40, 41), (28, 45, 53), (11, 60, 61), (16, 63, 65), (33, 56, 65), (48, 55, 73

Do the following lengths make a right triangle, acute triangle or obtuse triangle? (8 , 12, 15)

Multiple Choice

Using the Pythagorean Theorem, find the length of the missing side of the triangle pictured:

• 23
• 17
• 7

Multiple Choice

Using the Pythagorean Theorem, find the length of the missing side of the triangle pictured:

• 13
• 17
• 7

Multiple Choice

If a triangle has sides that measure 3 cm, 4 cm and 5 cm - is it a RIGHT triangle?

• Yes, right triangle
• No, not a right triangle

Multiple Choice

If a triangle has sides that measure 4 in, 5 in and 6 in - is it a RIGHT triangle?

• Yes, right triangle
• No, not a right triangle

Multiple Choice

What is the formula used for the Pythagorean Theorem?

• a + b = c
• a² + b² = c²
• a₂ + b₂ = c₂
• a x b = c

Multiple Choice

Why do we use the Pythagorean Theorem?

• To find the missing side of a right triangle
• To find the area of a triangle
• To find the volume of a cone
• To find the circumference of a circle

This equation can help us find the missing side of a right triangle.

​

We can also use it to determine if a triangle is a right triangle or not since it only works for right triangles. ​

​

Multiple Choice

Which side is the hypotenuse?

• this side

• that side

• this other side

Multiple Choice

Which equation below is a correct interpretation of the Pythagorean Theorem for the right triangle pictured on the left? Remember, the hypotenuse is always the longest side of a right triangle.

• $$x^2+y^2=z^2$$  

• $$y^2+x^2=z^2$$  

• $$x^2+z^2=y^2$$  

• $$y^2+z^2=x^2$$  

Multiple Choice

In the right triangle pictured on the left, which of the following equations will allow you to successfully solve for the unknown x?

• $$8^2+x^2=4^2$$  

• $$4^2+8^2=x^2$$  

• $$x^2+8^2=4^2$$  

• $$x^2+4^2=8^2$$  

​ 1. Write your equation

2. Square your numbers

3. Combine like terms

4. Take the Square Root​

​

Solving for the hypotenuse

1. Write the equation

2. Square your numbers

3. Subtract to get variable alone

4. Take the square root​

​

Solving for a leg

Multiple Choice

Which equation would you use to solve for x?

• $$6^2+x^2=8^2$$  

• $$6^2+8^2=x^2$$  

• $$x^2+8^2=6^2$$  

Multiple Choice

Which equation would you use to solve for x?

• $$13^2+x^2=5^2$$  

• $$5^2+13^2=x^2$$  

• $$x^2+5^2=13^2$$  

Multiple Choice

Determine the length of the missing side.

• 7

• 8

• 17

• 23

Multiple Choice

Level 2

Solve for the value of y

• 13

• 5

• 23

• 10

Legs and Hypotenuse

The legs ( "a" and "b") are always the two shorter sides

The hypotenuse ("c") is always the longest side

Multiple Choice

What is the missing side

• The Hypotenuse

• The Leg

The sides highlighted in red is the Hypotenuse for each right triangle.

The Converse of the Pythagorean Theorem

If the sum of the squares of the legs in a triangle equal to the square of the hypotenuse then you have a right triangle.

Multiple Choice

Is this a right triangle?

• Yes

• No

Multiple Choice

A 13 ft ladder touches a wall 12 feet above the ground. What is the distance from the wall to the base of the ladder?

• 5

• √12

• √169

• 6

Multiple Choice

Find the hypotenuse in the image shown

• 15 cm

• 20 cm

• 10 cm

• 9 cm

Multiple Choice

Can a right triangle have sides of length

5, 12, and 13?

• Yes.

• No.

Multiple Choice

Can a right triangle have sides of length

3, 6, and 9

• yes

• no

Multiple Select

The missing side is

• a leg

• the hypotenuse

Multiple Choice

Which of these measures is the length of the hypotenuse?

• 5

• 13

• 12

Multiple Choice

Look at the model of the Pythagorean Theorem. What is the length of the side of the large green square?

• 14 cm

• 15 cm

• 16 cm

• 13 cm

Multiple Choice

If the given side lengths form a triangle, then classify the triangle as acute, right, or obtuse.

6, 9, 15

• Acute

• Right

• Obtuse

Multiple Choice

If the given side lengths form a triangle, then classify the triangle as acute, right, or obtuse.

10, 12, 15

• Acute

• Right

• Obtuse

Multiple Choice

solve for c

• 7
• 9
• 4
• 13

Multiple Choice

You need a ladder that will reach up a 25 foot tall house when placed 10 feet away from the house. How tall does the ladder need to be?

• 25 feet
• 26 feet
• 27 feet
• 28 feet

Multiple Choice

solve for the value of y

• 13
• 5
• 23
• 10

Multiple Choice

The diagonal of a rectangle is 25 in. The width is 15 in. What is the length of the rectangle?

• 20 inches

• 29.2 inches

• 400 inches

• 625 inches

Multiple Choice

Casey travels from her house directly west to the bank and then directly north from the bank to the mall. She then travels home on the road connecting the mall and her house. What is her total distance traveled?

• 17 miles
• 32 miles
• 37 miles
• 40 miles

Multiple Choice

Which set of sides would make a right triangle?

• 4,5,6
• 8,10,12
• 5,12,13
• 5,10,12

Multiple Choice

Which of the following sentences would belong in the proof that describes this image?

• The sum of the areas of the two smaller squares is equal to the area of the large square.
• The sum of the side lengths of the two smaller squares is equal to the side length of the large square.
• The difference of the areas of the two smaller squares is equal to the area of the large square.
• The differences of the side lengths of the two smaller squares is equal to the side length of the large square.

Multiple Choice

You need a ladder that will reach up a 25 foot tall house when placed 10 feet away from the house. How tall does the ladder need to be?

• 25 feet
• 26 feet
• 27 feet
• 28 feet

Multiple Choice

What is the hypotenuse of a right triangle if the two legs measure 4 in and 5 in?

• √⁴¹
• 3
• 2√3
• 2√41

Multiple Choice

We are given one of the sides and the hypotenuse.

Find the length of the missing side length.

(Hint: distance from the wall to the bottom of the ladder)

• 7

• 5

• 11

• 25

Multiple Choice

Casey travels from her house directly west to the bank and then directly north from the bank to the mall. She then travels home on the road connecting the mall and her house. What is her total distance traveled?

• 17 miles
• 32 miles
• 37 miles
• 40 miles

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

What is side c called?

• Leg

• Hypotenuse

• $$90\degree\$$ angle

Multiple Choice

What is side a and b called?

• Legs

• Hypotenuse

• $$90\degree\$$ angle

Lets work one together

Multiple Choice

Use the Pythagorean Theorem to solve for x.

• $$\sqrt{1213}=34.8$$

• $$\sqrt{455}=21.3$$

• $$\sqrt{87}=9.3$$

• $$\sqrt{49}=7$$

Let's work this one together!

NOTE: You are not solving for the hypotenuse!

Multiple Choice

What side of the right triangle is the x on?

• Leg

• Hypotenuse

• Right Angle

Multiple Choice

Use the Pythagorean Theorem to solve for x.

• $$\sqrt{1295.06}=35.98$$

• $$\sqrt{565.4}=23.8$$

• $$\sqrt{49.6}=7.04$$

• $$\sqrt{11.4}=3.38$$

Multiple Choice

Which equation is set up correctly for this word problem?

• $$23^2+b^2=10^2$$

• $$10^2+b^2+23^2$$

• $$10^2+23^2=c^2$$

• $$a^2+23^2=c^2$$

Pythagorean Theorem

Pythagorean Theorem

a² + b² = c²

Find the missing side

Multiple Choice

Find the missing side.

• 9

• 10

• 12

• 100

Find the missing leg

​

Find the missing side - leave answer in radical form

​

Multiple Choice

Find missing side

• $$2\sqrt{5}$$

• $$\sqrt{20}$$

• $$2\sqrt{3}$$

Multiple Choice

Find the missing side length.

• $$\sqrt[]{73}\ cm$$  

• $$\sqrt[]{17}\ \ cm$$  

• $$73\ \ cm$$  

• $$\sqrt[]{13}\ \ cm$$  

Multiple Choice

Find the missing side length.

• $$\sqrt[]{5}\ ft$$  

• $$\sqrt[]{493}\ ft$$  

• $$\sqrt[]{31}\ ft$$  

• $$\sqrt[]{155}\ ft$$  

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

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

Word Problems

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

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

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

If you are solving to find a missing leg, should you add or subtract?

• Add

• Subtract

Multiple Choice

If you are solving to find a missing hypotenuse, should you add or subtract?

• Add

• Subtract

Multiple Choice

Find the missing side.

• 11

• 12

• 13

• 14

The Pythagorean Theorem

Hypotenuse

• The longest side of a right triangle

• The side that is opposite (across) from the 90^o angle.

• When using the Pythagorean Theorem, the Hypotenuse is represented by the variable, c.

Leg (of a Triangle)

• The two shorter sides of a right triangle

• The sides that are adjacent to the 90^o angle.

• When using the Pythagorean Theorem, the Legs are represented by the variables, a & b.

Right Triangle

• A right triangle is a triangle with a right angle in it (an angle that is 90^o)

• A triangle can be shown to have a 90^o angle by using a box.

• A right triangle will ALWAYS satisfy the Pythagorean Theorem

• undefined 

Is it a Right Triangle?

Multiple Choice

Is this a right triangle?

• Yes

• No

Multiple Choice

Is this a right triangle?

• Yes

• No

Multiple Choice

Is this a right triangle?

• Yes

• No

Multiple Choice

Is a triangle with side lengths of 12, 9, and 15 a right triangle?

• Yes

• No

Multiple Choice

Is a triangle with side lengths of 7, 4, and 4 a right triangle?

• Yes

• No

Multiple Choice

Find the missing side.

• 18

• 16

• 17

• 19

Multiple Choice

Find the missing side.

• 11

• 12

• 13

• 14

Multiple Choice

If three sides of a right triangle are 9, 40, and 41, which side is the hypotenuse?

• 9
• 40
• 41

Multiple Choice

Isabella has sticks that are 10cm, 11cm, and 13cm long.  Can she place the sticks together to form a right triangle?  Justify your answer.

• No, because 10+11 does not equal 13
• No, because 100+121 does not equal 169
• Yes, because there is a small side, medium side and long side
• Yes, because a triangle has 3 sides