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4.5 : Isosceles and Equilateral Triangles

4.5 : Isosceles and Equilateral Triangles. Objective: Students will be able to… U se and apply properties of isosceles and equilateral triangles. . Isosceles Triangles. 2 congruent legs Third side is the base The 2 congruent sides form the vertex angle

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4.5 : Isosceles and Equilateral Triangles

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  1. 4.5: Isosceles and Equilateral Triangles Objective: Students will be able to… Use and apply properties of isosceles and equilateral triangles.

  2. Isosceles Triangles • 2 congruent legs • Third side is the base • The 2 congruent sides form the vertex angle • The other 2 angles are the base angles. Vertex Angle Base Angles Legs BASE

  3. Isosceles Triangle Theorem If a triangle is isosceles, then the base angles are congruent. C A B

  4. Converse of Isosceles Triangle Theorem If 2 angles of a triangle are congruent, then the sides opposite the angles are congruent. (Therefore, it’s an isosceles triangle) C A B

  5. Find the value of the variables. y x 54⁰

  6. How do we know that triangle RST is isosceles? T U R W V S

  7. How do you know is isosceles? A B C

  8. Corollary: A statement that immediately follows a theorem. Corollary to the Isosceles Triangle Theorem: If a triangle is equilateral, then it is equiangular Corollary to converse of Isosceles Triangle Theorem: If a triangle is equiangular, then it is equilateral. B B C C A A

  9. Find the values of the variables. 1. 2. y° 60 x° 4x 60° 60 The perimeter is 54 cm. NOT DRAWN TO SCALE!!

  10. Find the value of the variables. The perimeter is 45 ft. (2x +1) (4y)

  11. THEOREM: The bisector of the vertex angle of an isosceles triangle is the perpendicular bisector of the base. C bisects A B D

  12. Find the values of the variables. 1. 2. x° y° x° 63° z 4 cm 65°

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