The Pythagorean Theorem

Multiple Choice

Which of the following is the correct equation for the Pythagorean theorem?

Open Ended

What are the steps to find the missing side length of a right triangle using the Pythagorean theorem?

Multiple Choice

Refer to your notes: Find the missing side length of the right triangle with sides 24 cm and 7 cm. Round to the nearest tenth if necessary.

• 25.0 cm

• 17.0 cm

• 23.0 cm

• 24.5 cm

Open Ended

Explain how you would use the Pythagorean theorem to solve for the missing side in a right triangle if you know the lengths of the other two sides.

Multiple Choice

Select all triangles where the Pythagorean theorem can be used to find the missing side length.

• A triangle with a right angle

• An equilateral triangle

• A triangle with no right angle

• A triangle with one angle greater than 90 degrees

Multiple Choice

Refer to your notes: Use the Pythagorean theorem to find the missing side length in the right triangle. Round to the nearest tenth if necessary. What is the length of the missing side?

• 8.0 yd

• 7.2 yd

• 9.2 yd

• 5.7 yd

Multiple Choice

Refer to your notes: A rectangular pool at Andy's gym measures 25 meters by 50 meters. How many meters would Andy need to swim in order to swim diagonally across the pool? Round to the nearest tenth when necessary.

• 55.9 meters

• 60.0 meters

• 65.0 meters

• 45.0 meters

Multiple Choice

Refer to your notes: A pole vaulter rests a 17-foot pole against a wall. If the top of the pole hits the wall 14 feet above the ground, how far from the wall is the bottom of the pole? Round to the nearest tenth when necessary.

• 10.2 ft

• 12.0 ft

• 8.5 ft

• 9.5 ft

Open Ended

Refer to your notes: If the area of square 2 is 64 units² and the area of square 3 is 36 units², find the area and the side length of square 1.

Open Ended

Refer to your notes: The squares below form a model of the Pythagorean theorem. Malachi has solved and found the area of the center square to be 527 square units. Describe his error and find the correct answer.

Fill in the Blanks

The hypotenuse is always the

side of a right triangle.

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

Find the missing side.

• 18

• 16

• 17

• 19

Multiple Choice

Determine the length of the missing side.

• 7

• 8

• 17

• 23

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

Level 4

Solve for x.

• 38.9

• 40.2

• 45.6

• 54

Multiple Choice

^{Find the length of the missing side}

• 48

• 108

• 83.6

• 72

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

Find the length of the missing side. 

• 20 in.
• 68 in.
• 16 in.
• 80 in.

Multiple Choice

A 10-foot ladder is leaning against the wall.  The bottom of the ladder is 4 feet from the base of the wall.  Which of the following is closest to the distance from the top of the ladder to the base of the wall?

• 9ft
• 11ft
• 6ft
• 14ft

Multiple Choice

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

• 12.12
• 21.2
• 7.3

Open Ended

Reflecting on what you learned today about the Pythagorean Theorem and the parts of a right triangle, what questions do you still have or what would you like to know more about?