8.G.B.4-Right On Target: Using the Pythagorean Theorem in 2D and 3D-student notes

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RIGHT

hypotenuse

longest

90

Multiple Choice

Which side is the hypotenuse?

• AB

• BC

• CA

Multiple Choice

Which side is the hypotenuse?

• AB

• BC

• CA

Multiple Choice

Which side is the hypotenuse?

• NE

• ND

• ED

Multiple Choice

The Pythagorean Theorem ONLY works on which type of triangle?

• obtuse

• scalene

• isosceles

• right

Multiple Choice

The Pythagorean Theorem is

a² + b² = c²

• false

• true

Multiple Choice

What is the opposite of squaring a number?

• divide
• multiply 
• fractions
• square root

Multiple Choice

Side c on a right triangle is ALWAYS the longest.

• true

• false

Multiple Choice

Side c on a right triangle is ALWAYS opposite of the right angle.

• true

• false

Multiple Choice

Sides a and b are called legs.

• true

• false

Multiple Choice

Side c is called the leg.

• true

• false

Multiple Choice

Side c is called the hypotenuse.

• true

• false

Multiple Choice

The Pythagorean Theorem is

c² = a² - b²

• false

• true

Multiple Choice

^{Which side is the c/hypotenuse?}

• AB

• BC

• CA

Multiple Choice

solve for c

• 7
• 9
• 4
• 13

Multiple Choice

Find the length of the missing side. 

• 25 cm
• 42 cm
• 52 cm
• 48 cm

a²

b²

c²

legs

hypotenuse

c²

 b² or a²

Multiple Choice

Do the segment lengths 9, 12, and 15 form a right triangle?

• Yes

• No

Multiple Choice

Find the length of the missing side

• 17

• 15

• 22

• 13

Multiple Choice

Find the length of the missing side

• 20

• 68

• 16

• 80

Multiple Choice

Find the length of the missing side

• 17

• 15

• 22

• 13

Multiple Choice

Is this a right triangle

• Yes

• No

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

What is the opposite of squaring a number

• divide

• multiply

• square root

• fractions

Multiple Choice

Sides a and b are called legs.

• true

• false

Multiple Choice

What is the name for side c?

• head

• body

• hippopotamus

• hypotenuse

Multiple Choice

What is the formula used to solve for the hypotenuse?

• a²⁺b²=c²
• a+b=c
• a-b=c
• c-a=c

Multiple Choice

Find the length of the missing side. 

• 25 cm
• 42 cm
• 52 cm
• 48 cm

measurement

RIGHT

consistent

Multiple Choice

A ladder is leaning against a wall. The foot of the ladder is 6 feet away from the wall, and the ladder reaches a point on the wall that is 10 feet above the ground. How long is the ladder?

• 8 feet

• 12 feet

• 14 feet

Multiple Choice

A square garden has a length of 24 feet and a diagonal of 26 feet. What is the width of the garden?

• 10 feet

• 12 feet

• 14 feet

Multiple Choice

A baseball diamond is a square with sides of 90 feet. What is the shortest distance, to the nearest foot, between first base and third base?

• 127 feet

• 128 feet

• 129 feet

Multiple Choice

The bottom of a 15 foot pole is 9 feet away from the wall and leaning. How high above the ground does the top of the pole reach on the wall?

• 12 feet

• 8 feet

• 6 feet

Multiple Choice

A television screen measures 50 inches diagonally and has a width of 30 inches. What is the height of the screen?

• 40 inches

• 20 inches

• 10 inches

Multiple Choice

A kite string is 100 feet long. If the kite is flying directly above a point on the ground that is 60 feet away from you, how high is the kite?

• 80 feet

• 40 feet

• 20 feet

Multiple Choice

A ramp is used to load goods onto a truck. The ramp is 5 feet high and reaches 13 feet along the ground from the back of the truck. How long is the ramp? (Round to the nearest whole number)

• 12 feet

• 14 feet

• 16 feet

Multiple Choice

A square frame has an area of 64 inches. What is the length of the diagonal of the frame?

• 11.3 inches

• 8 inches

• 18 inches

Multiple Choice

A square playground has an area of 100 square feet. What is the length of the diagonal measurement of the playground?

• 14.1 feet

• 4.5 feet

• 141.4 feet

Multiple Choice

A rectangular pool measures 20 feet in width and 40 feet in length. If a rope is stretched from one corner of the pool to the opposite corner, what is the length of the rope? (Round to the nearest whole number)

• 45 feet

• 50 feet

• 60 feet

Multiple Choice

A cyclist rides 30 miles due east and then 40 miles due north. To the nearest mile, how far is the cyclist from the starting point?

• 50 miles

• 60 miles

• 70 miles

rectangular prisms

cubes

space (see next slide)

multiple

​A space diagonal is a line segment connecting two opposite vertices of a 3D rectangular prism (or cube) that passes through its interior

Multiple Choice

What is the distance the spooky spider travels if it crawls up the entire diagonal inside the coffin.

• 2 units
• 6 units
• 100 units
• 32 units

Multiple Choice

What is the approximate width of the base?

• 7 ft
• 5 ft
• 3 ft
• 2 ft

Multiple Choice

A swimming pool has the dimensions shown. Use x to represent the length of the diagonal that goes from the bottom corner to the top corner at the opposite end of the pool, as shown by the diagonal dotted line. What is the value of x? 

• 31.3
• 32.3
• 33.3
• 64

Multiple Choice

What is the approximate length of EC?

• 13
• 3.605
• 7.81
• 61

Multiple Choice

What is the approximate length of c?

• 3
• 1.732
• 1
• 2.449

Multiple Choice

What is the approximate length of the blue line?

• 6.56
• 23
• 45
• 3.32

Multiple Choice

What is the height of the cone? 

• 14 cm
• 8 cm
• 12 cm
• 13.9 cm

Multiple Choice

Kathleen's ice cream cone has a diameter of 9cm and a slant height of 7.5cm. What is the height of the ice cream cone?

• 5cm

• 6cm

• 9cm

• 12cm

Multiple Choice

The square base of the pyramid has an area of 144 square feet. If the slant height of the pyramid is 10 feet, what is the height of the pyramid?

• 7 feet

• 8 feet

• 16 feet

• 144 feet

Multiple Choice

An Egyptian pyramid has a square base that measures 80 meters on each side. If the height of the pyramid is 30 meters, what is the slant height of the pyramid?

• 26 meters

• 50 meters

• 74 meters

• 85 meters

longest

negative

reasonable

Multiple Choice

The Pythagorean Theorem ONLY works on which triangle? 

• Obtuse

• Right

• Acute

• Isosceles

Multiple Choice

Do the segment lengths 9, 12, and 15 form a right triangle?

• Yes

• No

Multiple Choice

Find the length of the side indicated in the triangle below:

• A

• B

• C

• D

Multiple Choice

The diagram shows three squares that are joined at vertices to form a right triangle.

Which statement is true?

• The sum of the areas of square A and square C is equal to the area of square B.

• The sum of the areas of square B and square C is equal to the area of square A.

• The sum of the areas of square of C and Square B and square A equal to the area of square C.

• The sum of the areas of square A and Square B is equal to the area of square C.

Multiple Choice

A teacher is showing his student Jacob to join three squares at their vertices to create the figure shown in the diagram.

The student will use small congruent square tiles to cover each region without any gaps or overlaps. Based on the information, which statement is true?

• The number of tiles needed to cover Square R is the same as the number of square tiles needed to cover Square G and Square M

• The number of tiles needed to cover Square G is the same as the number of tiles needed to cover both Square R and Square M.

• The number of tiles needed to cover Square M is the same as the number of square tiles needed to cover Square R and Square G.

Multiple Choice

Fill in the blank: The _______ of the squares on the legs is equal to the area of the square on the hypotenuse

• difference
• square root
• sum
• product

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

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

5³⋅5⁴

• 5⁷
• 5⁻¹
• 5¹²
• 5

Multiple Choice

Anything raised to a power of zero is always: 

• 0
• 1
• itself
• negative

Multiple Choice

(7.7 x 10²) + (3.1 x 10²)=

• 108

• 10,800

• 1,080

• -2500

Multiple Choice

Simplify the following expression:

(2a²b⁴z)(6a³b²z⁵)

• 8a⁵b⁶z⁶

• 12a⁶b⁸z⁵

• 12a⁵b⁶z⁶

• 8a⁶b⁸z⁵

Multiple Choice

Which expression is equivalent to :

Multiple Choice

Solve for the value of y

• 13

• 5

• 23

• 10