Understanding 45-45-90 Triangles

What makes a 45-45-90 triangle special?

• It has three equal sides.

• It is an equilateral triangle.

• It has two equal sides and a specific angle ratio.

• It is a scalene triangle.

What is the side length ratio for a 45-45-90 triangle?

• a, a, a√3

• a√2, a, a

• a, a, a√2

• a, a√2, a

If one leg of a 45-45-90 triangle is 8, what is the length of the hypotenuse?

• 8√2

• 8

• 16

• 4√2

Given a leg of 20 in a 45-45-90 triangle, what is the length of the hypotenuse?

• 10√2

• 40

• 20√2

• 20

If the hypotenuse of a 45-45-90 triangle is 5√2, what is the length of each leg?

• 5

• 5√2

• 10

• 2.5√2

What is the first step in finding the legs of a 45-45-90 triangle when given the hypotenuse?

• Subtract √2 from the hypotenuse

• Multiply the hypotenuse by √2

• Divide the hypotenuse by √2

• Add the hypotenuse to √2

When given a hypotenuse of 4 in a 45-45-90 triangle, what is the value of each leg after rationalizing the denominator?

• 2√2

• 4√2

• 4

• 2

Why is it important to rationalize the denominator in a 45-45-90 triangle?

• To make calculations easier

• To avoid having a radical in the denominator

• To simplify the hypotenuse

• To change the triangle type

What is the simplified form of 4/√2 after rationalizing the denominator?

• √2

• 4√2

• 2√2

• 2

What is the final step in solving for a leg when given the hypotenuse in a 45-45-90 triangle?

• Multiply by √2

• Divide by √2

• Subtract √2

• Add √2