Question 1102886: True or false: It is not possible to prove one pair of triangles congruent and then use their congruent corresponding parts to prove another pair congruent.
Hi, everyone! Can anyone answer this question for me, please? I have never heard or learned anything about this. My textbook does not have any information in regards to it, either, and all the resources I have gone to do not have anything useful. I feel like it's false, but I honestly just don't know. If you could help me out, I would greatly appreciate it.
Thanks so much,
RR :)
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! The wording does not quite mean anything,
but what I think was meant to ask is
"if we use some parts of two triangles to prove they are congruent,
can we then use that to prove that
a pair of corresponding parts not used before are congruent?"
The answer is
Yes, of course,
Corresponding Parts of Congruent Triangles are Congruent,
which teachers usually abbreviate as CPCTC.
For example, if we find that
side AB is congruent with side DE,
side BC is congruent with side EF, and
angle ABC is congruent with angle DEF,
we can prove that triangles ABC and DEF are congruent
by Side-Angle-Side (SAS) congruence.
We then, by CPCTC, can conclude that other pairs of corresponding parts are congruent:
side AB is congruent with side DE,
angle BCA is congruent with angle EFD, and
angle CAB is congruent with angle FDE.
It was possible (by CPCTC) to prove those last 3 congruence statements,
after proving the triangles congruent.
The expected answer is FALSE.
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