This equations covers Worked Example 2 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 7 of 11 in this topic. Use this equations to connect the idea to the wider topic before moving on to questions and flashcards.

Worked Example 2

In the diagram, M is the midpoint of AB. Angle ACM = angle BCM = 90°. Prove triangle ACM is congruent to triangle BCM.

AM = BM    (M is the midpoint of AB)
Angle AMC = angle BMC = 90°    (given)
CM = CM    (common side)
Therefore triangle ACM ≅ triangle BCM    (SAS or RHS — both valid here)

Practice questions for Congruence

Which of the following is NOT a valid congruence condition for triangles?

A. SSS (three sides equal)
B. SAS (two sides and the included angle equal)
C. AAA (three angles equal)
D. RHS (right angle, hypotenuse and one side equal)

1 markfoundation

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.

3 marksstandard

Quick recall flashcards

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.

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.

Worked Example 2

Worked Example 2

Practice questions for Congruence

Quick recall flashcards

15 questions on Congruence — practise free