Pythagorean Theorem & Converse with basic Special triangles and

What is the length of the missing side?

• 17
• 13
• 10.9
• 169

Can side lengths 6, 8, and 10 form a right triangle?

• yes
• no

If the area of a square is 81, what is the length of the side?

• 9
• -9
• 20.25

Given these side lengths, classify the triangle.

• Acute

• Obtuse

• Right

• Not a triangle

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.

The slide at the playground has a height of 6 feet. The base of the slide measured on the ground is 8 feet. What is the length of the slide?

• 8 feet

• 5.29 feet

• 10 feet

• 14 feet

Match the following for finding sides in a 30-60-90 right triangle.

• Short leg times square root of 3

• Long Leg

• Half of the hypotenuse

• Short Leg

• Double the short leg

• Hypotenuse

Match the following for a 30-60-90 right triangle

• Opposite the right angle.

• Long Leg

• Opposite the 30° angle.

• Short Leg

• Opposite the 60° angle.

• Hypotenuse

In a 45-45-90 right triangle, how many sides are the same size?

• None

• Two

• All 3

• Depends on the triangle

Label each of the following.

a

b

c

Short Leg

Hypotenuse

Long Leg