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.

Submitted by Bractals

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Solution: (Hide)

/ABC = /DEF > 90° (1) implies /BCA, /EFD < 90° (2)
From the law of sines,
|AB| sin(/ABC) sin(/BCA) = ---------------- |AC| |DE| sin(/DEF) = ---------------- |DF| = sin(/EFD) (3)
(2) and (3) imply
/BCA = /EFD (4)
(1) and (4) imply
/CAB = /FDE (5) (5), |AB| = |DE|, and (1) imply that triangles ABC and DEF are congruent by ASA.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Another Approach (spoiler)	Harry	2010-11-02 13:44:38
By construction (spoiler)	Steve Herman	2010-11-01 16:06:54

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