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4.6 Isosceles, Equilateral and Right s
Isosceles triangle’s special partsA is the vertex angle (opposite the base) B and C are base angles (adjacent to the base) Leg Leg C B Base
Thm 4.6 Base s thm A If seg AB @ seg AC, then B @ C ) ( B CIf 2 sides of a then the s opposite them the base s of an isosceles are ) A If seg seg AC, then C ) ( B C
Thm 4.7 Converse of Base s thmIf 2 s of a the sides opposite them A If B @ C, then seg seg AC ) ( C B
Corollary to the base s thmIf a triangle is equilateral, then it is equiangular. A If seg seg seg CA, then C B C
Corollary to converse of the base angles thmIf a triangle is equiangular, then it is also equilateral. A ) If C, then seg seg seg CA ) B ( C
Example: find x and y X=60 Y=30 Y X 120
Thm 4.8 Hypotenuse-Leg (HL) @ thmA If the hypotenuse and a leg of one right to the hypotenuse and leg of another right , then the s _ B C _ Y _ X _ If seg seg XZ and seg seg YZ, then XYZ Z
Given: D is the midpt of seg CE, BCD and FED are rt s and seg BD @ seg FD. Prove: BCD @ FED
Proof Statements D is the midpt of seg CE, BCD and <FED are rt s and seg to seg FD Seg seg ED BCD FED Reasons Given Def of a midpt HL thm
Are the 2 ? ( 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
Find x. ) 56ft ( 8xft ) )) 56=8x 7=x ((
Determination of an Angle || A B C D MP ON Given triangles ∆ABC and ∆ADC, having AB=AC=AD in a square □ MNOP. Line N C = C O, and BD is parallel to NO.
4.6 Isosceles Triangles What you’ll learn: 1.To use properties of isosceles triangles 2.To use properties of equilateral triangles.
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8.Bottom left corner at (0,0), rest of coordinates at (2, 0), (0, 2) and (2, 2) 9. Coordinates at (0,0), (0, 1), (5, 0) or (0,0), (1, 0), (0, 5) 10. Using.
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