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**4.6 Isosceles, Equilateral and Right s**

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**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

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**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

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**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

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**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

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**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

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

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**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

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

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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

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

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

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

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