8.1: Right Triangles

8.1: Right Triangles Pythagorean Theorem Properties of Special Right Triangles

What is the Pythagorean Theorem used for? • to find the length of a missing side in a right triangle n 5 4

Pythagorean Theorem Formula a2 + b2= c2 c represents the hypotenuse a and b represent the legs

a Leg Where is it located??? c Hypotenuse Always opposite of the 90 degree angle b Leg

Remember!!! • The Pythagorean Theorem can ONLY be used on Right Triangles. • The Legs are ALWAYS the sides ADJACENT (next to) the 90 degree angle. • C is ALWAYS the Hypotenuse (the slant). • The Hypotenuse is ALWAYS opposite the 90 degree angle.

h 2 4 What is the length of the hypotenuse in the triangle below? a2 + b2= c2

h 2 4 Plug in the value for each variable in the formula. a2 + b2= c2 22 + 42= h2

What is the length of the hypotenuse in the triangle below? h 2 4 a2 + b2 = c2 22 + 42 = h2 4 + 16 = h2 20 = h2

What is the length of the hypotenuse in the triangle below? h 2 4 a2 + b2 = c2 22 + 42 = h2 4 + 16 = h2 20 = h2 = h 20 = h 2 5

Try this one . . . Find the hypotenuse of the right triangle below? 4 6 h

Find the hypotenuse of the right triangle below? 42 + 62 = h2 42 + 62 = h2 16 + 36 = h2 16 + 36 = h2 52 = h2 52 = h2 = h = h 52 52 7.21 = h 7.21 = h a2 + b2 = c2 4 6 h

Try this one . . . What is the length of the missing leg in the triangle below? 5 3 a2 + b2 = c2 x

Find the hypotenuse of the right triangle below? a2 + b2 = c2 32 + x2 = 52 5 3 9 + x2 = 25 -9 - 9 x x2 = 16 x = 16 x = 4

8.1: Right Triangles