Side Lengths Form a Right Triangle

State if the three side lengths form an acute, obtuse, or right triangle.

• Acute Triangle

• Right Triangle

• Obtuse Triangle

• Not a Triangle

What is the longest side of a right triangle called?

• Leg A

• Leg B

• Hypotenuse

• Pythagoras' Big Buddy

Casey travels from her house directly west to the bank and then directly north from the bank to the mall. She then travels home on the road connecting the mall and her house. What is her total distance traveled?

• 17 miles

• 32 miles

• 37 miles

• 40 miles

Can side lengths 3, 4, and 5 form a right triangle?

• yes

• no

Answer explanation

$3^2+4^2=5^2\ ?$
$9+16=25\ ?$
$25\ =\ 25$
This is true, so the side lengths do form a 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

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.

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.

Define a Pythagorean Triple

• When all three sides of a right triangle are whole numbers

• Three sides are equal lengths

• Two sides are equal in length

• When you add every number together to find the missing length

Answer explanation

A Pythagorean Triple:
When all three sides of a right triangle are whole numbers

Example: 3, 4, 5

$3^2+4^2=5^2$
$9+16=25$
$25\ =\ 25$

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.