Identifying Right Triangles

Identifying Right Triangles

Today we will:

Be able to figure out if a triangle is a right triangle by checking if its side lengths fit the Pythagorean Theorem

Right Triangles

- Have a 90 degree angle

- The side across from the right angle is called the hypotenuse. It is the longest side

- The other two sides are called legs

Multiple Choice

Which equation is the Pythagorean Theorem?

• $a^2+b^2=c^2$

• $a+b=c$

The Pythagorean Theorem

• For ALL right triangles, the Pythagorean Theorem applies

Refresher

• Legs: 7 and 3

• What is the length of the hypotenuse?

•  $a^2+b^2=c^2$  

The Pythagorean Theorem

• For ALL right triangles, the Pythagorean Theorem applies

• How can we use the Pythagorean Theorem to figure out if a triangle is a right triangle or not, given the side lengths?

Practice

We will determine if triangles ARE or ARE NOT right triangles

Triangle A

• Leg Lengths: 6 and 8

• Hypotenuse Length:  $\sqrt{100}$  

• This IS a right triangle

Triangle B

• Leg Lengths: 10 and 3

• Hypotenuse Length:  $\sqrt{120}$  

• This IS NOT a right triangle

Triangle C

• Leg Lengths: 2 and 6

• Hypotenuse Length:  $\sqrt{40}$  

• This IS a right triangle

Triangle D

• Leg Lengths: 13 and 11

• Hypotenuse Length:  $\sqrt{305}$  

• This IS NOT a right triangle

Multiple Choice

Triangle E
Leg lengths: 5 and 9
Hypotenuse length:  $\sqrt{100}$ 

• This IS a right triangle

• This IS NOT a right triangle

Triangle F

• Leg Lengths: 4 and 4

• Hypotenuse Length:  $\sqrt{16}$  

• This IS NOT a right triangle

• What kind of triangle is this?

Triangle G

• Leg Lengths: 15 and 5

• Hypotenuse Length:  $\sqrt{250}$  

• This IS a right triangle

Triangle H

• Leg Lengths: 11 and 11

• Hypotenuse Length:  $\sqrt{242}$  

• This IS a right triangle

Multiple Choice

Triangle J
Leg lengths: 4 and 7
Hypotenuse length:  $\sqrt{65}$ 

• This IS a right triangle

• This IS NOT a right triangle

Today we:

Were able to figure out if a triangle is a right triangle by checking if its side lengths fit the Pythagorean Theorem