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4.6 Isosceles, Equilateral and Right s. Isosceles triangles special parts A is the vertex angle (opposite the base) B and C are base angles (adjacent.

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Presentation on theme: "4.6 Isosceles, Equilateral and Right s. Isosceles triangles special parts A is the vertex angle (opposite the base) B and C are base angles (adjacent."— Presentation transcript:

1 4.6 Isosceles, Equilateral and Right s

2 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

3 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 ) (

4 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

5 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

6 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

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

8 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

9 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

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

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

12 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

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


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