Exploring Congruent Triangles
Overview
Two figures are congruent when they have the same shape and the same size, and for triangles that means every matching side and every matching angle is congruent. The key skill of this lesson is correspondence: a congruence statement such as △ABC ≅ △QRS names the vertices in matching order, and that order tells you exactly which parts correspond. From it flows CPCTC — corresponding parts of congruent triangles are congruent — the principle that lets you pull any needed side or angle measure out of a congruence statement.
Vocabulary
- Congruent Figures
- Figures that have the same shape and the same size. Congruence is not affected by translating, rotating, or reflecting a figure.
- Congruent Triangles
- Two triangles are congruent if and only if their corresponding parts are congruent — all three pairs of corresponding sides and all three pairs of corresponding angles.
- Corresponding Parts
- The sides and angles of two figures that occupy the same relative position. In a congruence statement, corresponding vertices are named in the same position in both names.
- Congruence Statement
- A statement such as △ABC ≅ △QRS that names two congruent figures with their vertices listed in corresponding order: A corresponds to Q, B corresponds to R, and C corresponds to S.
- CPCTC
- Corresponding Parts of Congruent Triangles are Congruent. Once two triangles are known to be congruent, any pair of corresponding sides or angles must be congruent.
Main Ideas
- Congruent means same shape and same size: every corresponding side and angle matches exactly.
- Always write congruence statements in corresponding order. The first triangle can be named starting at any vertex, but the second must follow the same correspondence.
- Read parts off a statement by position: in △ABC ≅ △QRS, side AB corresponds to side QR, and ∠B corresponds to ∠R.
- CPCTC turns a congruence statement into six facts — three pairs of congruent sides and three pairs of congruent angles.
- Moving a figure by a translation, rotation, or reflection never changes its size or shape, so the image is always congruent to the original.
Lesson Notes
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Lesson Video
Watch the lesson video.
Interactive Activity
Explore congruent triangles, name corresponding parts, and use CPCTC.
Practice Problems
Want More Practice?
Download the practice worksheet for this lesson, work the problems, then check your work with the solutions.