Pythagorean Theorem Determine Right Triangle

What is the formula for Pythagorean theorem?

• a²⁺b²=c²

• a+b=c

• a-b=c

• c-a=c

The Pythagorean Theorem ONLY works on which triangle? 

• obtuse

• scalene

• isosceles

• right

Which statement is the MOST accurate about the converse of the Pythagorean Theorem?

• The converse is used to determine an unknown side length.

• The converse is only useful with right triangles

• The converse is used to determine if a triangle is or is not a right triangle

• The converse always works out that a²+b²=c²

Answer explanation

The Converse of the Pythagorean Theorem states:

IF
$a^2+b^2=c^2$
(where c is the longest side length)

THEN

The triangle is a right triangle.

Given the 3 lengths of a triangle are 6 in, 8 in and 10 in. Will this make a right triangle?

• yes

• no

Answer explanation

$6^2+8^2=10^2\ ?$
$36+64=100\ ?$
$100\ =\ 100$
This is true, so the side lengths do form a right triangle.

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

• 19.3

• 25

• 16.6

What would you use to solve for x?

• Pythagorean Theorem

• Trig

• Inverse Trig

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.

On your own paper, write an equation using the Pythagorean Theorem and solve for x.

• x = 6724

• x = 77.9

• x = 82

• x = 98

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.

• x = 6724

• x = 77.9

• x = 82

• x = 98