Warm-up 1.An isosceles triangle has ________. 2.Find the value of x. xoxo xoxo two congruent sides 45 o

7.4 Special Right Triangles Use properties of special triangles.

45 o – 45 o – 90 o 45 o – 45 o – 90 o triangle is an isosceles right triangle. It can be formed by cutting a square in half. 45 o

1.Prove: c = Prove x = Given:

Theorem 7.8: 45 o – 45 o – 90 o Triangle Theorem In a 45 o – 45 o – 90 o triangle, the hypotenuse is times as a long as each leg. Hypotenuse = leg *

Example 1: Find the hypotenuse in a 45 o – 45 o – 90 o triangle a)b)

Example 2: Find the legs x x x x 30 a)b)

Example 3: Standardized Test Practice MNP is a right triangle. Find the length of MP. a)18 in b) c)36 in d) M PN 18 in 45 o

Guided Practice Find the value of the variable d 4.Find the leg of a 45 o – 45 o – 90 o triangle with a hypotenuse of 6. 1)2) 3)