4.6 Isosceles, Equilateral and Right  s Pg 236

Standards/Objectives: Standard 2: Students will learn and apply geometric concepts Objectives: Use properties of Isosceles and equilateral triangles. Use properties of right triangles.

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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) A B C Leg Base

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

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

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

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

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

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

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

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

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