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Topic: POW Solution, Jan. 24-28
Replies: 0

 Problem of the Week Posts: 292 Registered: 12/3/04
POW Solution, Jan. 24-28
Posted: Feb 1, 1994 3:29 PM

*********************************************************************
Problem of the Week for January 24-28

Consider the two triangles below (note that they aren't to scale):

A
/ . O
/113 . . \
7 / . 10 7 . 113 \
/ . . \
/ . . \
/ . . 27 40\
/ 40 27 . G ------------------------- D
C ---------------------------------- T 10

a) How many pairs of equal sides and angles do the two triangles have?
b) Are the two triangles congruent? Explain.

extra: Can you find two noncongruent triangles with six pairs of
equal sides and angles (with no side or angle paired more
than once)? Explain.

*********************************************************************

We received one and a half correct answers to this week's problem.
The correct and complete solution was received from

Daniel Chan, Grade 10, Burnaby South Secondary School, Burnaby, BC

An additional solution of "The triangles are not congruent" was

************************

From: "Jim Swift" <jswift@cln.etc.bc.ca>

The following solution cam from Daniel Chan, a Grade 10 student at Burnaby
South Secondary School, Burnaby, BC

>a) How many pairs of equal sides and angles do the two triangles have?
The triangles have three pairs of equal angles and two pairs of equal
sides.
>b) Are the two triangles congruent? Explain.
No, none of the conditions of congruence are satisfied. The pairs of
equal sides are not opposite the pairs of equal angles.
>extra: Can you find two noncongruent triangles with six pairs of
> equal sides and angles (with no side or angle paired more
> than once)? Explain.

It is not possible, because triangles with three pairs of equal sides
are congrunent.
Jim Swift
Burnaby South 2000 S. S.
jswift@cln.etc.bc.ca