Solving for the Sides in Pythagorean Theorem

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.

Does the set of numbers represent a Pythagorean Triple? (Use the Pythagorean Theorem Converse)

• Yes

• No

Answer explanation

$4^2+5^2=6^2\ ?$
$16+25=36\ ?$
$41\ne36$
The left and right side of the equation are not equal, so these side lengths do not form a right triangle.

What is the formula for Pythagorean theorem?

• a²⁺b²=c²

• a+b=c

• a-b=c

• c-a=c

If three sides of a right triangle are 9, 40, and 41, which side is the hypotenuse?

• 9

• 40

• 41

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

• yes

• no

Do the segment lengths 9, 12, and 15 form a right triangle?

• Yes

• No

Is this triangle a right triangle?

• yes

• no

What are the 2 shorter sides of a right triangle called?

• Hypotenuse

• Pythagorean Theorem

• Legs

• Right triangle

Do these 3 side lengths form a right triangle?
13, 80, and 81?

• yes

• no

What is the final step in solving this work for c?
a² + b² = c²
3² + 4² = c²
9 + 16 = c²
25 = c²

• Divide both sides by 2

• Take the square root of both sides