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