1. Two Special Right Triangles
45°- 45°- 90°
30°- 60°- 90°

3. Hypotenuse Leg Leg 45°- 45°- 90°
A 45°- 45°- 90° triangle has two legs and a hypotenuse.
45°
Hypotenuse
Leg
Leg

4. Hypotenuse 45°- 45°- 90° The hypotenuse is opposite the right angle.

5. Hypotenuse Leg a Leg a 45°- 45°- 90°
The legs are equal because they are opposite equal angles.
45°
Hypotenuse a
Leg
Leg a

6. Hypotenuse a2 Leg a Leg a 45°- 45°- 90° The hypotenuse is 2 of a leg

7. 45°- 45°- 90°
COPY THIS INTO YOUR NOTEBOOK!
45° a
a2 a

8. 45°- 45°- 90° Practice
Let's Try
Some Problems

9. 45°- 45°- 90° Practice 4
45°
4 2 4
SAME
leg*2

10. 45°- 45°- 90° Practice 9
45°
9 2 9
SAME
leg*2

11. 45°- 45°- 90° Practice 2
45°
2 2 2
SAME
leg*2

12. 45°- 45°- 90° Practice
Now Let's
Go Backward

13. 45°- 45°- 90° Practice
45°
3 2
hypotenuse2

14. 45°- 45°- 90° Practice
45°
3 2 3 3
SAME
hypotenuse2

15. 45°- 45°- 90° Practice
45°
6 2
hypotenuse2

16. 45°- 45°- 90° Practice
45°
6 2 6 6
SAME
hypotenuse2

17. 45°- 45°- 90° Practice
45°
11 2
hypotenuse2

18. 45°- 45°- 90° Practice
45°
112 11 11
SAME
hypotenuse2

19. 30°- 60°- 90° Triangles
SOMETHING
DIFFERENT

20. The 30-60-90 triangle has a hypotenuse, a short leg, and a long leg.
30°- 60°- 90°
The triangle has a hypotenuse, a short leg, and a long leg.
30°
60°
Long Leg
hypotenuse
Short Leg

21. The hypotenuse is opposite the right angle.
30°- 60°- 90°
The hypotenuse is opposite the right angle.
30°
60°
hypotenuse

22. The long side is opposite the 60 degree angle. Long Leg
30°- 60°- 90°
The long side is opposite the 60 degree angle.
30°
60°
Long Leg
hypotenuse

23. The short leg is opposite the 30 degree angle. Long Leg
30°- 60°- 90°
The short leg is opposite the 30 degree angle.
30°
60°
Long Leg
hypotenuse
Short Leg

24. 2a a 30°- 60°- 90° Practice The hypotenuse is twice the short leg. 30°

25. 2a a a3 30°- 60°- 90° Practice The long leg is 3 of the short leg

26. COPY THIS INTO YOUR NOTEBOOK! 2a
30°- 60°- 90°
60°
30°
COPY THIS INTO YOUR NOTEBOOK! 2a
a3 a

27. 30°- 60°- 90° Practice
60°
30°
The key is to find the length of the short side. 8
43
Hypotenuse = short leg * 2 4
Long Leg = short leg * 3

28. 10 53 5 30°- 60°- 90° Practice Hypotenuse = short leg * 2
Long Leg = short leg * 3

29. 14 73 7 30°- 60°- 90° Practice Hypotenuse = short leg * 2
Long Leg = short leg * 3

30. 30°- 60°- 90° Practice
Now Let's
Go Backward

31. 22 113 11 30°- 60°- 90° Practice Short Leg = Hypotenuse  2
Long Leg = short leg * 3

32. 4 23 2 30°- 60°- 90° Practice Short Leg = Hypotenuse  2
Long Leg = short leg * 3

33. 18 93 9 30°- 60°- 90° Practice Short Leg = Hypotenuse  2
Long Leg = short leg * 3

34. 30 153 15 30°- 60°- 90° Practice Short Leg = Hypotenuse  2
Long Leg = short leg * 3

35. 46 233 23 30°- 60°- 90° Practice Hypotenuse = Short Leg * 2
Short Leg = Long leg   3

36. 28 143 14 30°- 60°- 90° Practice Hypotenuse = Short Leg * 2
Short Leg = Long leg   3

37. 32 163 16 30°- 60°- 90° Practice Hypotenuse = Short Leg * 2
Short Leg = Long leg   3

38. YOUR WORK
Answer the following questions from your textbook. They will be collected and graded!
Pg 485 #3-5
Pg 486 #7-12