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Published byPatrick Reynolds Modified over 2 years ago

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4.6 Isosceles, Equilateral and Right s

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Isosceles triangles special parts A is the vertex angle (opposite the base) B and C are base angles (adjacent to the base) A B C Leg Base

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

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

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

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

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Thm 4.8 Hypotenuse-Leg (HL) thm If the hypotenuse and a leg of one right are to the hypotenuse and leg of another right, then the s are. _ _ _ _ A BC X Y Z If seg AC seg XZ and seg BC seg YZ, then ABC XYZ

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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 B C D F E

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Proof Statements 1.D is the midpt of seg CE, BCD and

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

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

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

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