10-6 Converse of the Pythagorean Theorem

The Converse of Pythagorean Theroem

Learning Goal: Students will apply the converse of the Pythagorean Theorem to determine if three given side lengths form a right triangle.

Math Response

Gravel used for construction purposes is piled in the approximate shape of a cone.

What is the approximate radius of the cone?

Type answer here

Correct Answer: 15

Deg^°

Rad

Math Response

A plane takes off from an airport and travels 13 miles on its path. If the plane is 11 miles from its takeoff point horizontally, what is the height? Round to the nearest tenth if necessary.

Type answer here

Correct Answer: 6.9

Deg^°

Rad

Math Response

A 12-foot flagpole is placed in the center of a square area. To stabilize the pole, a wire will stretch from the top of the pole to each corner of the square. The flagpole is 7 feet from each

corner of the square.

What is the length of each wire? Round to the nearest tenth.

Type answer here

Correct Answer: 13.9

Deg^°

Rad

Math Response

Leslie and Cindy went to swim at the town swimming pool. If Leslie wanted to swim diagonally from one corner of the pool to the other, what is the distance she will have to swim?

Type answer here

Correct Answer: 50

Deg^°

Rad

Open Ended

A construction worker is measuring the frame for a roof to ensure that it creates a right triangle.

Part A: Determine whether the triangle is a

right triangle.

Part B: Justify your reasoning.

Open Ended

​DeSean is riding his bike through a park on a triangular path. The distances of his path are 8 miles, 15 miles, and 17 miles.

Part A: Does DeSean’s triangular path form a right triangle? 

Part B: Justify your reasoning. Explain, in word, why this is or is not a right triangle.

Multiple Choice

Phillis wants to ensure the sides of her garden create a right angle. Determine whether the triangle is a right triangle.

• yes

• no

Multiple Choice

The Mighty Motorcycle Club president designs a bike jump. The jump forms a triangle with dimensions of 15 feet, 26 feet, and 36 feet. Is the triangle formed by the bike jump a right triangle?

• yes

• no

Open Ended

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

Justify your reasoning. Explain, in word, why this is or is not a right triangle.

Open Ended

Given the 3 lengths of a triangle are 6 in, 8 in and 10 in.

Will this make a right triangle?

Justify your reasoning. Explain, in word, why this is or is not a right triangle.

Multiple Select

Which two sets of side lengths does not form a right triangle?

• 38, 80, 90

• 16, 63, 65

• 36, 77, 85

• 14, 15, 29

Multiple Choice

Which set of sides would make a right triangle?

• 4,5,6

• 8,10,12

• 5,12,13

• 5,10,12

Open Ended

Does this triangle form a right triangle?

Justify your reasoning.

The sides of the triangle are 10, 24, and 26.

Multiple Choice

1. The _______ of a right triangle is the side of the triangle that is opposite the right angle.

• GCF

• Angle

• Hypotenuse

• all of the above

Open Ended

Use what we know about the pythagorean theorem to determine if this triangle is a right triangle. Write a statement explaining why this is or is not a right triangle. Show your work to justify your answer. 

Multiple Choice

A 10 ft. ladder is leaning against a wall. The bottom of the ladder is 4 ft. away from the base of the wall. The distance between the top of the ladder and the base of the wall is _____.

• $$\sqrt[]{46}$$  ft.

• $$\sqrt[]{84}$$  ft.

• $$\sqrt[]{69}$$  ft.

• $$\sqrt[]{35}$$  ft.

Fill in the Blanks

Multiple Choice

Solve for the length of the diagonal within the rectangular prism.

• 25

• 169

• 5

• 13

Multiple Choice

What is the diagonal length of the iPad?

• 9.2 in
• 11 in
• 13 in
• 9.6 in

Multiple Choice

What is the area of the third square?

• 6.7 cm²
• 33.5 cm²
• 2025 cm²
• 45 cm²

Math Response

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?

Type answer here

Correct Answer: 40

Deg^°

Rad

Multiple Choice

A soccer field is a rectangle 100 meters wide and 130 meters long. The coach asks players to run from one corner to the other corner diagonally across. What is the distance? Round your answer to the nearest whole number.

• 30 meters

• 83 meters

• 164 meters

• 260 meters

Dropdown

The pythagorean theorem can only be used on ​

Select answer

triangles.

​End of lesson.