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Sections 4-5 & 4-6 Isosceles, Equilateral and Right s Pg 228 Isosceles triangle’s special parts A is the vertex A angle (opposite the base) B and C are base angles (adjacent to the base) B C Base Thm 4.3 Base s thm • If 2 sides of a are @, the the s opposite them are @.( the base s of an isosceles are @) A If seg AB @ seg AC, then B @ C B C Thm 4.4 Converse of Base s thm • If 2 s of a are @, the sides opposite them are @. A If B @ C, then seg AB @ seg AC B C Corollary to the base s thm A corollary is a statement that follows immediately from a theorem. • If a triangle is equilateral, then it is equiangular. If seg AB @ seg BC @ seg CA, then A @ B @ C B A C Corollary to converse of the base angles thm ) • If a triangle is equiangular, then it is also equilateral. A If A @ B @ C, then seg AB @ seg BC @ seg CA B ( C Example: find x and y • X=60 • Y=30 X 120 Y Thm 4.8 Hypotenuse-Leg (HL) @ thm If seg AC @ seg XZ and seg BC @ seg YZ, then ABC @ XYZ _ B C _ Y _ X A _ • If the hypotenuse and a leg of one right are @ to the hypotenuse and leg of another right , then the s are @. Z Given: D is the midpt of seg CE, BCD and FED are rt s and seg BD @ seg FD. Prove: BCD @ FED B C F D E Proof Statements 1. D is the midpt of seg CE, BCD and <FED are rt s and seg BD @ to seg FD 2. Seg CD @ seg ED 3. BCD @ FED Reasons 1. Given 2. Def of a midpt 3. HL thm Are the 2 triangles @ ? Yes, ASA or AAS ) ( Find x and y. x 75 y 60 90 y x 2x + 75=180 2x=105 x=52.5 y=75 x x=60 y=30 Find x. 56ft ( 8xft )) 56=8x 7=x (( Assignment Practice Worksheets (PRWS) 4-5 Isosceles and Equilateral Triangles 4-6 Congruence in Right Triangles