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Congruent triangles (ASA and AAS)

I can appreciate and use the criteria by which triangles are congruent (ASA and AAS).

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Lesson 9 of 18

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Year 9

Congruent triangles (ASA and AAS)

I can appreciate and use the criteria by which triangles are congruent (ASA and AAS).

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Lesson details

Key learning points

By knowing two angles and a length in the triangle and image, you can prove congruence.
The angle pairs must be identical.
This rule is derived from the SAS criteria for congruence.

Keywords

Congruent - If one shape can fit exactly on top of another using rotation, reflection or translation, then the shapes are congruent.

Common misconception

Pupils may struggle to spot congruent triangles if they only look for ASA.

Encourage pupils to add any further information to diagrams, like the third angle, before starting to prove congruence.

Pupils will need to construct triangles during this lesson, using a ruler and protractor. You may wish to practice drawing angles and checking pupils are considering what type of angle they are drawing.

Teacher tip

Licence

This content is © Oak National Academy Limited (2026), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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Prior knowledge starter quiz

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6 Questions

Q1.
Which line segment has not been drawn to the same length as the other two?

Correct Answer: An image in a quiz

Q2.
The angle marked $$x°$$ is °.

Correct Answer: 73, seventy three, 73°, seventy-three

Q3.
The missing angle in triangle XYZ is °.

Correct Answer: 33, thirty three, thirty-three, 33°

Q4.
Triangle ABC is congruent to triangle XYZ, therefore YZ = cm.

Correct Answer: 8.2, 8.2cm, 8.2 cm

Q5.
Triangle ABC and triangle XYZ are congruent, therefore is 9.6 cm.

Correct Answer: YZ, ZY

Q6.
All __________ are similar.

Correct answer: squares

rectangles

Correct answer: equilateral triangles

rhombi

Correct answer: circle

Assessment exit quiz

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6 Questions

Q1.
The criteria ASA (angle-side-angle) and AAS (angle-angle-side) are equivalent. True or false?

Correct answer: True - if you know two angles in a triangle then you can calculate the third.

False - one is where you know the side between two angles and the other isn't.

Q2.
Triangle ABC and triangle XYZ are congruent by AAS/ASA. Which angle in triangle XYZ is 46°?

∠YXZ

Correct answer: ∠XZY

It doesn't matter

Q3.
Match each triangle on the top row to the triangle on the bottom row that it is congruent to.

Correct Answer:a,d

Correct Answer:b,f

Correct Answer:c,e

Q4.
Which of the following triangles is not guaranteed to be congruent to the other three triangles?

Correct Answer: An image in a quiz

Q5.
Which of these quadrilaterals can be split into two congruent triangles using one diagonal?

Correct answer: square

Correct answer: rectangle

Correct answer: kite

trapezium

Correct answer: parallelogram

Q6.
Complete this congruence proof. ∠ABD = ∠BDC as they are given in the diagram, BD is a shared edge and ∠ADB = ∠DBC as they are equal angles, so triangle ABD and BDC are congruent by SAS.

Correct Answer: alternate, interior alternate

Lesson appears in

UnitMaths / Geometrical properties: similarity and Pythagoras' theorem

Maths

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Congruent triangles (ASA and AAS)

Congruent triangles (ASA and AAS)

Lesson slides

Lesson details

Key learning points

Keywords

Common misconception

Licence

Lesson video

Worksheet

Prior knowledge starter quiz

6 Questions

Q1.Which line segment has not been drawn to the same length as the other two?

Q2.The angle marked $$x°$$ is °.

Q3.The missing angle in triangle XYZ is °.

Q4.Triangle ABC is congruent to triangle XYZ, therefore YZ = cm.

Q5.Triangle ABC and triangle XYZ are congruent, therefore is 9.6 cm.

Q6.All __________ are similar.

Assessment exit quiz

6 Questions

Q1.The criteria ASA (angle-side-angle) and AAS (angle-angle-side) are equivalent. True or false?

Q2.Triangle ABC and triangle XYZ are congruent by AAS/ASA. Which angle in triangle XYZ is 46°?

Q3.Match each triangle on the top row to the triangle on the bottom row that it is congruent to.

Q4.Which of the following triangles is not guaranteed to be congruent to the other three triangles?

Q5.Which of these quadrilaterals can be split into two congruent triangles using one diagonal?

Q6.Complete this congruence proof. ∠ABD = ∠BDC as they are given in the diagram, BD is a shared edge and ∠ADB = ∠DBC as they are equal angles, so triangle ABD and BDC are congruent by SAS.

Lesson appears in

UnitMaths / Geometrical properties: similarity and Pythagoras' theorem

Maths

Q1.
Which line segment has not been drawn to the same length as the other two?

Q2.
The angle marked $$x°$$ is °.

Q3.
The missing angle in triangle XYZ is °.

Q4.
Triangle ABC is congruent to triangle XYZ, therefore YZ = cm.

Q5.
Triangle ABC and triangle XYZ are congruent, therefore is 9.6 cm.

Q6.
All __________ are similar.

Q1.
The criteria ASA (angle-side-angle) and AAS (angle-angle-side) are equivalent. True or false?

Q2.
Triangle ABC and triangle XYZ are congruent by AAS/ASA. Which angle in triangle XYZ is 46°?

Q3.
Match each triangle on the top row to the triangle on the bottom row that it is congruent to.

Q4.
Which of the following triangles is not guaranteed to be congruent to the other three triangles?

Q5.
Which of these quadrilaterals can be split into two congruent triangles using one diagonal?

Q6.
Complete this congruence proof. ∠ABD = ∠BDC as they are given in the diagram, BD is a shared edge and ∠ADB = ∠DBC as they are equal angles, so triangle ABD and BDC are congruent by SAS.