Congruent triangles

Definition

Two triangles are congruent if all their corresponding sides and angles are equal. You can prove congruence with one of four conditions: SSS, SAS (the angle between the two sides), AAS, or RHS for right-angled triangles. Three equal angles (AAA) only prove similarity.

Worked example

If AB = DE, BC = EF and B̂ = Ê, then △ABC ≡ △DEF (SAS).

Two right-angled triangles with equal hypotenuses and one other equal side are congruent (RHS).

Where it appears in the exam

Congruent triangles is part of the geometry section of CAPS Grade 9 Mathematics and appears in school tests and the end-of-year exam.

Step-by-step method

1. Mark the equal sides and angles on the diagram.
2. Match the corresponding vertices in order.
3. Check which condition the equal parts fit: SSS, SAS, AAS or RHS.
4. Write the congruence statement with the reason.

Common mistake

Using SSA (two sides and an angle that is not between them), which does not prove congruence.

Related geometry terms

• Hypotenuse
• Midpoint theorem

Frequently asked questions

What does congruent triangles mean in Grade 9 Maths?

Two triangles are congruent if all their corresponding sides and angles are equal. You can prove congruence with one of four conditions: SSS, SAS (the angle between the two sides), AAS, or RHS for right-angled triangles. Three equal angles (AAA) only prove similarity.

When do you learn about congruent triangles?

Congruent triangles is taught in the geometry section of CAPS Grade 9 Mathematics and is used again in Grades 10 to 12.

How do I practise questions involving congruent triangles?

Snap a question that uses congruent triangles into Snap&Learn with your grade set to Grade 9, or work through the Grade 9 topic guide and practice papers.