Tuesday, February 3, 2009

Elearn Geometry Problem 241: Triangle with Equilateral triangles, Congruence

Problem: Triangle with Equilateral triangles, Parallelogram

See complete Problem 241 at:
gogeometry.com/problem/p241_triangle_equilateral_congruence_sas.htm

Level: High School, SAT Prep, College geometry

Post your solutions or ideas in the comments.

2 comments:

  1. In triangles ABA' and C'BC we have C'B = AB & BC = BA'(sides of equilateral triangles) while the included angle in each case is angle (ABC+60) Thus the two triangles are congruent. So AA' = CC'
    Ajit: ajitathle@gmail.com

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  2. See the drawing

    - ∠CBC’=∠ABC+∠ABC’= ∠ABC+60°
    - ∠ABA’= ∠ABC+∠CBA’= ∠ABC+60°
    - =>∠CBC’=∠ABA’
    - ΔABA’ is congruent to ΔCBC’ (SAS)
    - Therefore AA’=CC’

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