1. 7.3 Special Right Triangles

2. Objectives Use properties of 45° - 45° - 90° triangles

3. 45° - 45° - 90°∆
Theorem 7.6
In a 45°- 45°- 90° triangle, the length of the hypotenuse is √2 times the length of a leg.
hypotenuse = √2 • leg
45 °
x√2
45 °
**Note in any isosceles triangle, the angles opposite the congruent sides are congruent

4. EX 3: Find x.

5. EX1: Find a.

6. EX 2: Find b.

7. 30° - 60° - 90°∆
Be sure you realize the shorter leg is opposite the 30° & the longer leg is opposite the 60°.
Theorem 7.7
In a 30°- 60°- 90° triangle, the length of the hypotenuse is twice as long as the shorter leg, and the length of the longer leg is √3 times as long as the shorter leg.
60 °
30 °
x√3
Hypotenuse = 2 ∙ shorter leg Longer leg = √3 ∙ shorter leg

8. EX 4: Find BC and CD.

9. EX 5: Find BD and CD

10. EX 6: Find FE and FG.

11. EX 7: Find HI and IJ.

12. EX 8: Find a, b, c, x, and y

13. EX 9: Triangle ABC is equilateral with a perimeter of 51
EX 9: Triangle ABC is equilateral with a perimeter of 51. Find the length of its altitude.

14. Assignment
Regular: Workbook 7-3: 1-10, 13 p. 360; Honors: Workbook 7-3: 1-10, 13 p. 360; 12-23