Edexcel IGCSE Math B 6.J Triangle congruence Question Bank

Practise proving triangle congruence in geometric diagrams using equal sides, included angles, midpoints and common lengths.

Exam points

link midpoint, square, equilateral or isosceles facts to matching sides in two triangles
choose a valid congruence condition and support each equal side or angle with a reason
use common sides or included angles to complete a proof of congruent triangles

[Maximum number: 3]

Figure for Question 6.J Triangle congruence question 1 — Edexcel IGCSE Math B

The diagram shows a square ABCD.
M is the midpoint of AD.
N is the midpoint of AB.
Prove that $\triangle DAN$ is congruent to $\triangle CDM$ .

Valid congruence statements include:

AD=DC
because ABCD is a square.

AN=DM
because N and M are midpoints of AB and AD.

$\angle DAN=\angle CDM=90^\circ$
because the angles are right angles in the square.

Therefore $\triangle DAN\cong\triangle CDM$ by SAS.

M2 for two correct statements with reasons.
M1 for one correct statement with reason, or all three statements with no reasons.
A1 for SAS/RHS/SSS stated with all three correct reasons.

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6.J Triangle congruence question 1