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.

## Tuesday, February 3, 2009

### Elearn Geometry Problem 241: Triangle with Equilateral triangles, Congruence

Labels:
congruence,
equilateral,
sas,
triangle

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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'

ReplyDeleteAjit: ajitathle@gmail.com

See the

ReplyDeletedrawing- ∠CBC’=∠ABC+∠ABC’= ∠ABC+60°

- ∠ABA’= ∠ABC+∠CBA’= ∠ABC+60°

- =>∠CBC’=∠ABA’

- ΔABA’ is congruent to ΔCBC’ (SAS)

- Therefore

AA’=CC’