Pythagorean Theorem4.08

Do Now Remember the pattern for right

triangles:

Area of small square+

Area of medium square=

Area of large square

Do Nowa) 3 in. , 5 in., and 8 in. 9 + 25 = 64 34 ≠ 64 not a right triangleb) 3 m, 4 m, and 5 m 9 + 16 = 25 25 = 25 right trianglec) 4 cm, 6 cm, and 8 cm 16 + 36 = 64 52 ≠ 64 not a right triangle

1) Find the missing value

9 + 34 = ?? = 43

8 + 12 = ?? = 20

10 + ? = 25? = 15

Pythagorean Theorem The relationship that we have

discovered between the sides of right triangles is called the Pythagorean Theorem.

It allows us to determine if a triangle is a right triangle and to find missing side lengths when we know that the triangle is a right triangle.

Right Triangle Vocabulary legs =

› the sides that create the right angle› “hold up” the right angle like legs to a

table› the two shorter sides

leg

leg

Right Triangle Vocabulary hypotenuse =

› the side across from the right angle› does not touch the right angle› the longest side of the triangle

hypotenuse

Pythagorean Theorem area of small square + area of

medium square = area of large square

leg² + leg² = hypotenuse²

Pythagorean Theoremor

a² + b² = c²

Example5² + x² = 13²25 + x² = 169-25 -25 x² = 144

x = 12 12 cm

x

5 cm

13 cm

3) Find the missing side Don’t forget to identify the legs and

hypotenuse

Plug the values into the formula

Solve

Get a star after each row is completed