1. 4.6 Isosceles, Equilateral and Right s

2. Isosceles triangle’s special parts
A is the vertex angle (opposite the base)
 B and C are base angles (adjacent to the base)
Leg
Leg C B
Base

3. Thm 4.6 Base s thm A If seg AB @ seg AC, then  B @  C ) ( B C
If 2 sides of a  then the s opposite them the base s of an isosceles  are ) A
If seg seg AC, then   C ) ( B C

4. Thm 4.7 Converse of Base s thm
If 2 s of a  the sides opposite them A
If  B @  C, then seg seg AC ) ( C B

5. Corollary to the base s thm
If a triangle is equilateral, then it is equiangular. A
If seg seg seg CA, then C B C

6. Corollary to converse of the base angles thm
If a triangle is equiangular, then it is also equilateral. A )
If C, then seg seg seg CA ) B ( C

7. Example: find x and y
X=60
Y=30 Y X
120

8. Thm 4.8 Hypotenuse-Leg (HL) @ thmA
If the hypotenuse and a leg of one right  to the hypotenuse and leg of another right , then the s _ B C _ Y _ X _
If seg seg XZ and seg seg YZ, then   XYZ Z

9. Given: D is the midpt of seg CE, BCD and FED are rt s and seg BD @ seg FD. Prove:  BCD @  FED

10. Proof
Statements
D is the midpt of seg CE,  BCD and <FED are rt  s and seg to seg FD
Seg seg ED
 BCD   FED
Reasons
Given
Def of a midpt
HL thm

11. Are the 2 ? (
Yes, ASA or AAS ) ) ( ( (

12. Find x and y. y x 60 75 90 y x x x=60 2x + 75=180 2x=105 x=52.5 y=30

13. Find x. )
56ft (
8xft ) ))
56=8x
7=x ((