# Congruent shapes

Shapes that are exactly the same size and shape. One can be moved onto the other by sliding, turning or flipping.

Maths (school) · Part 07: Shape and space · Card 5 of 9 · Last updated 2026-10-19

## Analogy

Like two identical biscuits cut from the same cutter.

## Example

**Congruence rules for triangles**

SSS: three sides equal
SAS: two sides and the angle between
ASA: two angles and a side
RHS: right angle, hypotenuse, side

## In practice

Mass-produced parts, like car doors, must be congruent.

## Practice

### Flashcards

- **Name the four congruence rules for triangles.** SSS, SAS, ASA and RHS.

## Questions people ask

### How can you prove two triangles are congruent?

Show that one of the four rules holds: SSS, SAS, ASA, or RHS for right-angled triangles. You only need one rule, and you must give the reason for each equal part. AAA (three equal angles) is not enough. Write the matching corners in the same order so the equal parts are easy for a marker to follow.

### Why is AAA not enough to prove congruence?

Three equal angles only guarantee the same shape, not the same size. A small triangle and a big triangle can have identical angles. Those are similar triangles. For congruence, at least one side length must also match. Think of a small and large photocopy of the same triangle: same angles, different sizes.

## Related concepts

- [Similar shapes](https://studyvisually.com/learn/science/maths-school/maths-school-part-7/maths-school-part-7-concept-6)
- [Bearings](https://studyvisually.com/learn/science/maths-school/maths-school-part-7/maths-school-part-7-concept-7)
- [Vectors](https://studyvisually.com/learn/science/maths-school/maths-school-part-7/maths-school-part-7-concept-8)
- [Constructions](https://studyvisually.com/learn/science/maths-school/maths-school-part-7/maths-school-part-7-concept-9)

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