Pythagorean Theorem, Pythagorean Converse, Special Right Triangles

Find the length of side a.

Where is the hypotenuse located in a right triangle?

• Always the top side

• Always the bottom side

• Always the side opposite the right angle

• Always the side that is touching the right angle

What type of special triangle is this?

• 45°-45°-90°

• 30°-60°-90°

• Not enough information provided

• Equilateral

In this 45-45-90 triangle, I have been given the length of a leg.  How do I find the length of the hypotenuse?

• It is the same length as the given leg.

• Multiply that leg's length by 2.

What is the length of y in this 45-45-90 triangle?

Which side is the short leg of this 30-60-90 triangle?

• 6

• m

• n

• Not enough information provided

I have been given the short leg (4) in this 30-60-90 triangle.  How do I find the long leg?

• Multiply 4 by 2

• Divide 4 by 2

Find the value of x.

What is the length of the missing side?

• 17

• 13

• 10.9

• 169

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.