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Understanding Isosceles Triangles: Properties and Theorems

Explore the properties and theorems related to isosceles triangles, including congruent sides, base angles, equiangular angles, and equilateral triangles. Learn how to apply AAS and explore corollaries to base angle theorems.

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Understanding Isosceles Triangles: Properties and Theorems

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  1. The two congruent sides of an isosceles triangle. The angle made by the intersection of the legs of an isosceles triangle The non-congruent side of an isosceles triangle (Base does NOT mean it's got to be at the bottom) The angles formed by the base and legs of an isosceles triangle.

  2. ∠C AC F G

  3. equiangular equilateral equilateral equiangular 180 60 60

  4. equiangular equilateral JL 8 ∠MJL LJ 8 LJ 8 8 4

  5. ∠DCA Corollary to the equiangular Converse of Base Angles Theorem ∠ACB AAS ≅ Theorem

  6. ∠H ≅ ∠J 15 Since ∆DCA is equilateral and ∆DCA ≅ ∆BAC, both angles BAC and DAC are 60. m∠BAD = m∠BAC + m∠DAC m∠BAD = 60 + 60 m∠BAD = 120

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