Geometry Warm-Up 1/31/12

Find the value of x.

13

7

x

x12

151.

2.

Perfect Squares Quiz

12. 142

2. 172

3. 122

4. 52

5. 82

6. 192

7. 112

8. 12

9. 202

10. 162

11. 72

1. 42

13. 22

14. 102

15. 32

16. 182

17. 132

18. 92

19. 152

20. 62

Sec 8.3: Special Right Triangles

Geometry

January 31, 2012

Special Right Triangles

Special Right Triangles Triangles whose angles measures are

either 45-45-90 or 30-60-90.

45

45

A

B

C

30

60

E

F D

45-45-90 Triangle

Special Relationships Because you have two 45 angles,

the two legs are congruent. The hypotenuse is √2 times as long

as each legHypotenuse = √2 ● leg

45

45 hypotenuse

leg

leg

30-60-90 Triangles Special Relationships

Because the two acute angles have different measures, you have a long leg and a short leg

The hypotenuse is twice as long as the short leg and the long leg is √3 times as long as the short leg.

Hypotenuse = 2 ● short legLong Leg = √3 ● short leg

hypotenuse

short leg

long leg

30

60

E

F D

Example 1

Find the value of x.

7

x

7

45

Hypotenuse = √2 ● leg

x = √2 (7)

x = 7√2

Example 2

Find the values of s and t.

30

t

s

9

Long leg = √3 ● short leg

9 = √3 (s)

9√3 = s

3 3√3 = s

Hyp = 2 ● short leg

t = 2 (3√3)

t = 6√3