1. Special Right Triangles

2. 45-45-90 Right Isosceles Triangle Leg Hypotenuse Legs are congruent Hypotenuse = Legs =

3. 45-45-90 Right Isosceles Triangle s s Leg Leg Hyp 11 33 2 12

4. Leg 1-If the perimeter of the square is 28, what is the length of the diagonal? 2- If the diagonal has a length of 12, what is the perimeter of the square? Area? The diagonal of a square is the Hypotenuse of two isosceles right triangles. 1- Perimeter = 28 4x = 28 x = 7 Leg = 7 Hyp = 7  2 2- Diagonal = 12 Leg = 12÷  2 = 6  2 P = 4(6  2) =24  2 A = 6  2·6  2 = 72

5. 30-60-90 Long Leg Short Leg Hypotenuse Know the Short Leg (SL): Hypotenuse = 2 · SL Long Leg = Know Hypotenuse: Short leg = ½ Hypotenuse Know Long Leg (LL): Short leg = 30° 60°

6. 30-60-90 x 2x Short Leg Long Leg Hyp1 2 3 6 42 12 6 12 24 12

7. 30-60-90 When you draw the altitude of an equilateral triangle, you create two 30-60-90 triangles. The triangle side length is the hypotenuse of the 30-60-90. Half of the side length is the short leg of the 30-60-90. The altitude, then, is half the triangle side times the square root of 3. 60° 30° x 2x 30°