4.6 Isosceles, Equilateral and Right  s

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.

Assignment • pp. 239-240 #1-25 all • Chapter 4 Review – pp. 252-254 #1-17 all • Test after this section • Chapter 5 Postulates/Theorems • Chapter 5 Definitions • Binder Check

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

Thm 4.6Base 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 4.7Converse of Base s thm • If 2 s of a  are @, the sides opposite them are @. A If  B @ C, then seg AB @ seg AC ) ( C B

Corollary to the base s thm • If a triangle is equilateral, then it is equiangular. A If seg AB @ seg BC @ seg CA, then A @ B @C B 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 Y X 120

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

Given: D is the midpt of seg CE, BCD and FED are rt s and seg BD @ seg FD.Prove:  BCD @ FED B F D C E

Statements D is the midpt of seg CE,  BCD and <FED are rt  s and seg BD @ to seg FD Seg CD @ seg ED  BCD  FED Reasons Given Def of a midpt HL thm Proof

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

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

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

4.6 Isosceles, Equilateral and Right  s