Pythagorean Theorem Do Measurement Create a Right Triangle?

The measurements 3, 4, and 5 satisfy the converse of the Pythagorean Theorem and therefore form a right triangle. If each measurement is doubled, will the new triangle still be a right triangle? Select the choice that answers the question and has a valid argument that can be used to defend your solution.

A carpenter is measuring a cabinet to ensure the sides create a right angle.

• no

• yes

Three cities form a triangle. Tom measures the distances between the three cities on a map. The distances between the three cities are 45 miles, 56 miles, and 72 miles.

Is the triangle formed by the three cities a right triangle?

• no

• yes

Allie wants to make sure that the pieces of cloth for a costume are right triangles.

• no

• yes

Which measurement is closest to the value of d in inches?​ (a)  

• 14.3 in.

• 6.3 in.

• 4.0 in.

• 19.8 in.

Find the length of the missing side. 

• 17 cm

• 22 cm

• 15 cm

• 13 cm

How far above the ground doe the ladder touch the building?

Mathematical Equivalence

ON

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

• 19.31

• 25

• 16.58

Ethan and Zoe are building a treehouse and need to find the length of a ladder. Which equation would they use to solve for x?

• x²+6²=8.5²

• sin(8.5)= x/6

• sin(8.5)= 6/x

• sin^-1(6/8.5)

Answer explanation

Ethan and Zoe can use the Pythagorean theorem to find the length of the ladder (x). The equation x² + 6² = 8.5² represents the relationship between the ladder, the height, and the distance from the base.

Aiden and Aria are building a treehouse and need to find the length of the ladder (x) to reach the top. What magical math tool should they use to solve for x?

• Pythagorean Theorem

• Trig

• Inverse Trig

Answer explanation

Aiden and Aria can use the Pythagorean Theorem to find the length of the ladder (x). This theorem applies to right triangles, where the ladder acts as the hypotenuse, making it the correct tool for their problem.