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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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New
New
Year 9

Congruent triangles (ASA and AAS)

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

Download all resources
Share activities with pupils

Lesson details

Key learning points

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

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.

Keywords

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

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 (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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Starter quiz

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6 Questions

Q1.
Which line segment has not been drawn to the same length as the other two?
An image in a quiz
An image in a quiz
Correct Answer: An image in a quiz
An image in a quiz
Q2.
The angle marked $$x°$$ is °.
An image in a quiz
Correct Answer: 73, seventy three, 73°, seventy-three
Q3.
The missing angle in triangle XYZ is °.
An image in a quiz
Correct Answer: 33, thirty three, thirty-three, 33°
Q4.
Triangle ABC is congruent to triangle XYZ, therefore YZ = cm.
An image in a quiz
Correct Answer: 8.2, 8.2cm, 8.2 cm
Q5.
Triangle ABC and triangle XYZ are congruent, therefore is 9.6 cm.
An image in a quiz
Correct Answer: YZ, ZY
Q6.
All __________ are similar.
Correct answer: squares
rectangles
Correct answer: equilateral triangles
rhombi
Correct answer: circle

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°?
An image in a quiz
∠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.
An image in a quiz
Correct Answer:a,d

d

Correct Answer:b,f

f

Correct Answer:c,e

e

Q4.
Which of the following triangles is not guaranteed to be congruent to the other three triangles?
An image in a quiz
An image in a quiz
An image in a quiz
Correct Answer: An image in a quiz
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.
An image in a quiz
Correct Answer: alternate, interior alternate