See complete Problem 242 at:

gogeometry.com/problem/p242_triangle_equilateral_parallelogram.htm

Level: High School, SAT Prep, College geometry

Post your solutions or ideas in the comments.

## Tuesday, February 3, 2009

### Elearn Geometry Problem 242: Triangle with Equilateral triangles, Parallelogram

Labels:
congruence,
equilateral,
parallelogram,
triangle

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C'A = BA

ReplyDeleteangle C'AB' = Angle BAC = 60 - angle B'AB

AB' = AC

So, by SAS postulate,

triangle C'AB' is congruent to triangle BAC

So, C'B' = BC = BA'

Similarly as

triangle A'B'C is congruent to triangle BAC,

A'B' = BA = BC'

So,

in quadrilateral A'BC'B' both pairs of opposite sides are congruent.

So, it is a parallelogram.

http://img15.imageshack.us/img15/857/problem242a.png

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