Associated Topics || Dr. Math Home || Search Dr. Math

### Naming Corresponding Parts of Congruent Figures

Date: 04/23/2003 at 22:56:54
From:  John
Subject: Corresponding parts of congruent figures

Given triangle OPS congruent to triangle TQR, name the corresponding
sides and angles of the two triangles.

Date: 04/24/2003 at 08:49:14
From: Doctor Peterson
Subject: Re: Corresponding parts of congruent figures

Hi, John.

When we name triangles that are congruent, we name them both in the
order in which we consider parts to correspond. Your triangles might
look like this:

P                       Q
/  \                    /  \
/     \                 /     \
/        \              /        \
/           \           /           \
/              \        /              \
O-----------------S     T-----------------R

So among the vertices, O corresponds to T (in the same position at
lower left when they are lined up this way), and their angles SOP and
RTQ are the same. Among the edges, side OS corresponds to TR (on the
bottom in both), and they have the same length. You just have to list
the other two pairs of corresponding sides and the other two pairs of
corresponding angles.

Note that congruent triangles don't HAVE to be facing the same
direction; they might look like this instead:

P                 T-----------------R
/  \                \              /
/     \               \           /
/        \              \        /
/           \             \     /
/              \            \  /
O-----------------S           Q

Although TR is no longer on the bottom, it still corresponds to OS
because it is the side with the same length. You might picture tracing
OPS on a sheet of paper, labeling the vertices, and cutting it out.
Then slide it around so that the vertices O, P, and S lie on top of T,
Q, and R, respectively, in the other triangle, to show that they are
congruent. (In this case, you will also have to flip the paper over.)
Whatever "part" of TQR lies under any part of OPS is its corresponding
part.

Here is a discussion from the Dr. Math archives of how these ideas
apply in a proof:

Congruent Parts Congruent Triangles Congruent (CPCTC)
http://mathforum.org/library/drmath/view/55397.html

and here is an example where it is used:

Writing a Proof
http://mathforum.org/library/drmath/view/55312.html

If you have any further questions, feel free to write back.

- Doctor Peterson, The Math Forum
http://mathforum.org/dr.math/
Associated Topics:
High School Triangles and Other Polygons
Middle School Triangles and Other Polygons

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search

Ask Dr. MathTM
© 1994- The Math Forum at NCTM. All rights reserved.
http://mathforum.org/dr.math/