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📘 Lesson 5 of 16 · Geometry

🟰 Congruence

Two figures are congruent if they are exactly the same shape and size — one could be placed perfectly on top of the other after moving, flipping, or rotating it.

Course progress: 31%

01 Key Concepts

Congruent Figures

Figures with identical shape and size; all corresponding sides and angles are equal.

Congruence Notation

Written with a special symbol, but described in words as 'triangle ABC is congruent to triangle DEF', meaning every corresponding part matches.

SSS (Side-Side-Side)

If all three sides of one triangle equal all three sides of another, the triangles are congruent.

SAS (Side-Angle-Side)

If two sides and the angle between them match another triangle's two sides and included angle, the triangles are congruent.

ASA (Angle-Side-Angle)

If two angles and the side between them match another triangle's two angles and included side, the triangles are congruent.

CPCTC

'Corresponding Parts of Congruent Triangles are Congruent' — once triangles are proven congruent, every matching pair of sides and angles must be equal.

02 Solved Examples

Example 1 Triangle ABC has sides 5, 6, 7. Triangle DEF has sides 5, 6, 7. Are they congruent?
  1. All three corresponding sides match exactly.
  2. This satisfies the SSS congruence rule.
Answer: Yes, congruent by SSS
Example 2 Two triangles share two equal sides and the included angle between them is also equal. What congruence rule applies?
  1. Two sides plus the angle directly between them matches a specific named rule.
Answer: SAS (Side-Angle-Side)
Example 3 If triangle ABC is congruent to triangle DEF, and angle A = 50°, what is angle D?
  1. Congruent triangles have exactly matching corresponding angles (CPCTC).
  2. Angle D corresponds to angle A.
Answer: Angle D = 50°

03 Practice Questions

1If two triangles have all 3 sides equal, what rule proves congruence?
SSS
2If two triangles share 2 angles and the included side, what rule applies?
ASA
3What does CPCTC stand for?
Corresponding Parts of Congruent Triangles are Congruent
4Do congruent figures have to be the same size?
Yes
5Can congruent figures be mirror images of each other?
Yes, congruence allows flips (reflections)

📄 Congruence — Downloadable Worksheet

10 questions with a full answer key. Grab the PDF to print, or try the interactive version in your browser.

🗒 Cheat Sheet ⬇ Download PDF 🖥 Interactive Worksheet