1. Special Right Triangles
Section 7-3
spi.3.2.G
Jim Smith JCHS

2. Our First Special Right
Triangle Is A 3,4,5
The Hypotenuse Must Be
A Multiple Of 5 And
The Legs Must Be
Multiples Of 3 And 4

3. x x 3 5 3 5 25 + 25 = x² 9 + 9 = x² 50 = x² 18 = x² 50 = x 18 = x
Use The Pythagorean Theorem To Find X x x 3 5 3 5
= x²
50 = x²
50 = x
= x
9 + 9 = x²
18 = x²
18 = x
3 2 = x

4. Speed Trials 45, 45, 90
7 2
4 2 7 4 4 7
13 2
2 2 2 13 2 13

5. If 2 Sides Of A Triangle Are Congruent, Then The Angles Opposite
Them Are Congruent 45
45, 45, 90 | 45 |

6. 45, 45, 90
Legs are equal
Leg x 2 = hyp 45
X 2 | X 45 | X
Mult by 2

7. Going Backwards….DIVIDE8 2 = 8 2 = 8
4 2
4 2 45 8 2
4 2
Div by 2

8. 30, 60, 90 Triangles 60 Short 30 Long Hyp Leg Leg
No angles are equal so
no sides are congruent 60
Hyp
Short
Leg 30
Long
Leg

9. 30, 60, 90 Triangles
Mult by 2 60
Hyp
Short
Leg 30
Long
Leg

10. 30, 60, 90
2 x 8 = 16 60 8 30

11. 30, 60, 90
2 x 5 = 10 60 5 30

12. 30, 60, 90 60
Hyp
Short
Leg 30
Long
Leg
Mult by 3

13. 30, 60, 90 60
Hyp 15 30
15 x 3 = 15 3

14. 30, 60, 90 60
Hyp 3 30
3 x 3 = 3 3

15. 13 13 2 Going Backwards….DIVIDE 60 30 H SL LL
For now, we’ll leave it as an improper fraction

16. Going Backwards….DIVIDE
5 3 60
= 5 H SL 3 30 LL
5 3

17. Going Backwards….DIVIDE8 3 60 H 3 SL 30 LL 8 8 3 3 8 3 = 3

18. 30, 60, 90
10 3 3 12
9 3 2 9 5 30 30 30
6 3 9 2
5 3 3 6

19. What Do You
Know About
This Triangle? 60 30 30 | | 60 60 |