Warm Up Find the value of x. Leave your answer in simplest radical form. x 9 7 x

Special Right Triangles Objectives: To use the properties of 45-45-90 right triangles

45°-45°-90° Right Triangle THEOREM: What is it? It is an isosceles, right triangle– Both legs are congruent!! THEOREM: The hypotenuse is times the length of the legs.

45°-45°-90° Right Triangle IF YOU NEED TO FIND THE HYPOTENUSE: Multiply the leg by IF YOU NEED TO FIND A LEG: Divide the hypotenuse by

Examples #1 and #2 Find h: 2. Find x: x 9 h

Example #3 Find x: x

Example #4 - A square has a perimeter of 24 inches Example #4 - A square has a perimeter of 24 inches. How long is the diagonal?

7 x Warm up 1. Find x and y. 2. Find x. x y If you were absent on Friday… you should stay after school or go to the MATH LAB. Warm up 1. Find x and y. 2. Find x. x 7 y x

Special Right Triangles Objectives: To use the properties of 30-60-90 right triangles

30°-60°-90° Right Triangle Shorter Leg is the side opposite the 30° angle Longer leg is the side opposite the 60° angle Hypotenuse is ALWAYS opposite the 90° angle

If you need to find the shorter leg (side opposite 30°):

Examples: IF GIVEN THE SHORTER LEG OR THE HYPOTENUSE… YOU HIT THE 1. Example # 2

Examples: IF GIVEN THE LONGER LEG, then find the shorter leg First! 1. Example # 4

Example #5: Example # 5 1.

Example #6: Find the value of each variable. (Figure not drawn to scale) a=____ b=____ c=____ d=____

Example #7: Find the area of the triangle. What is the formula for area of a triangle?

Fill in the table of values for the side lengths of a 30-60-90 triangle: Shorter Leg Longer Leg Hypotenuse 3 4 15 34 10