# Prove triangles are congruent

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## Lesson details

### Key learning points

- In this lesson, we will learn how to prove that two triangles are congruent. We will investigate four different conditions involving observation and comparison of the angles and sides of each triangle. If any condition is met, we can determine that the triangles are congruent.

### Licence

This content is made available by Oak National Academy Limited and its partners and licensed under Oak’s terms & conditions (Collection 1), except where otherwise stated.

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### 3 Questions

Q1.

A

B

D

Q2.

A

D

Q3.

B

C

D

### 3 Questions

Q1.

ABCD is a parallelogram. Select the working that proves triangles ABC and BCD are congruent using the SSS conditions. Choose all that apply.

Opposite angles in a parallelogram are equal

Opposite lengths in a parallelogram are parallel

Q2.

ABCD is a parallelogram. Select the working that proves triangles ABC and BCD are congruent using the ASA conditions. Choose all that apply

∠ABD = ∠BDC and ∠ADB = ∠DBC as alternate angles are equal. AD = BC (opposite angles equal)

AB = DC and AD = BC as opposite lengths in a parallelogram are equal. ∠DAB = ∠BCD

BD is a shared side. AB = DC. ∠ABD = ∠BDC as alternate angles are equal.

Q3.

ABCD is a parallelogram. Select the working that proves triangles ABC and BCD are congruent using the SAS conditions. Choose all that apply.

∠ABD = ∠BDC and ∠ADB = ∠DBC as alternate angles are equal. AD=BC.

∠ABD = ∠BDC and ∠ADB=∠DBC as alternate angles are equal. BD is a shared side.