Naming Corresponding Parts of Congruent FiguresDate: 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/ |
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