# 4.6 Isosceles, Equilateral and Right s

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4.6 Isosceles, Equilateral and Right s

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

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

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

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

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

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

Thm 4.8 Hypotenuse-Leg (HL) @ thm
A 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

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

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

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

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

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