perplexus.info :: Geometry : Not ASA, SAS, or SSS

Not ASA, SAS, or SSS (Posted on 2010-11-01)

Given two triangles ABC and DEF which satisfy the following:

1) |AC| = |DF|
2) |AB| = |DE|
3) /ABC = /DEF > 90°

Prove or disprove that the triangles are congruent.

See The Solution Submitted by Bractals

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By construction (spoiler)

| Comment 1 of 2

They are congruent.

Let's construct triangle ABC.

1) Draw point and call it B.

2) Draw two line segments that end at point B and form an angle = /DEF.

3) Pick point A on one of the segments, such that |AB| = |DE|.

4) Using a compass, find point C on the other segment such that |AC| = |DF|. Because /DEF > 90°, |DF| is the longest side of the triangle, so there is only one possibility for C on the other segment. And because the choice of C is forced, the triangles are necessarily congruent.

Posted by Steve Herman on 2010-11-01 16:06:54

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