- Congruent shapes are identical in both shape and size. One can be placed exactly on top of the other (flips and rotations allowed).
- All corresponding sides are equal in length.
- All corresponding angles are equal in size.
- The symbol for congruence is ≅ (sometimes written ≡).
- Congruent ≠ Similar: Similar shapes have the same shape but may differ in size (they are enlargements of each other). Congruent shapes are a special case where the scale factor is exactly 1.
This key facts covers What Does Congruent Mean? within Congruence for GCSE Mathematics. Revise Congruence in Geometry & Measures for GCSE Mathematics with 15 exam-style questions and 12 flashcards. This is a high-frequency topic, so it is worth revising until the explanation feels precise and repeatable. It is section 2 of 11 in this topic. Use this key facts to connect the idea to the wider topic before moving on to questions and flashcards.
Practice questions for Congruence
Which of the following is NOT a valid congruence condition for triangles?
When writing a congruence statement, such as triangle ABC ≅ triangle PQR, explain what it tells you about the sides and angles of the two triangles.
Quick recall flashcards
SAS Congruence Condition
Side-Angle-Side: Two sides and the INCLUDED angle (the angle between the two sides) are equal.
The angle MUST be between the two sides — if it is not included, SAS does not apply.
SSS Congruence Condition
Side-Side-Side: All three pairs of corresponding sides are equal.
If AB = DE, BC = EF, and AC = DF, then the triangles are congruent.
Fixing three side lengths determines the triangle completely.