Checking and securing understanding of congruent triangles (ASA) | Maths

Starter quiz

Izzy says, "__________ shapes can fit exactly on top of another using rotation, __________ or __________ ." Select the words that correctly complete Izzy's statement.

congruent ✓

reflection ✓

similar

translation ✓

transformation
Some Oak pupils are discussing congruence. Which pupils are correct?

Andeep: Two triangles are congruent if they both have a right-angle.

Izzy: Two triangles are congruent if they have three angles the same.

Jacob: Two triangles are congruent if they have three edges the same. ✓

Jun: Two triangles are congruent if they have two edges and any angle the same.

Laura: "No, they must have two edges and the angle between them the same." ✓
Are triangle ABC and DEF congruent? Explain your answer.

No, the angles between the two equal sides is different.

Yes, they have two equal sides, so the 3rd side is also fixed.

Yes, the angles between the two equal sides are the same. ✓
Given these two triangles are congruent, find the length of the sides marked $x$ and $y$ .

Side $x$ is 6.3 cm

Side $x$ is 10.4 cm ✓

Side $y$ is 6.3 cm ✓

Side $y$ is 10.4 cm

Side $y$ is 13.1 cm
Given these two triangles are congruent, the angle marked $z$ is ______°.

'51' ✓
ABCD is a rhombus. Select the set of statements needed to prove that triangle ABD and triangle BCD are congruent.

AD = BC as the shape is a rhombus. Also, AB = CD ✓

BD is a common edge

Angle ADC = angle ABC as opposite angles in a rhombus are equal.

Angle BAD = angle BCD as opposite angles in a rhombus are equal. ✓

∴ triangle ABD and triangle BCD are congruent by SAS. ✓

Exit quiz

Two shapes will always be congruent if...

…they are enlargements of each other.

…they are reflections of each other. ✓

…they are similar to each other.

…they are transformations of each other.
Two triangles are guaranteed to be congruent if...

...they have 3 angles that are the same.

...they have any 2 angles that are the same .

...they have the same edge lengths. ✓

...two edges and any angle are the same.

...two angles and one corresponding edge are the same. ✓
Are these two triangle congruent? Explain your answer.

No, they are not congruent as the 7.3 cm edges are not corresponding. ✓

No, they are not congruent as the angles are in a different order.

Yes, they are congruent by SAS.

Yes, they are congruent by ASA.
These two triangles are congruent. Match each side length to its value.

$w$

⇔

7.2 cm ✓

$y$

⇔

8.3 cm ✓

$z$

⇔

5.8 cm ✓
Given these two triangles are congruent, the angle marked $x$ is ______°.

'50' ✓
In the diagram, ∠MNO = ∠PON and NQ = QO. Select the statements that are needed to prove that triangle MNO is congruent to triangle PNO.

As NQ = QO, then triangle NQO is an equilateral triangle. Hence ∠QNO = ∠QON

As NQ = QO, then triangle NQO is an isosceles triangle. Hence ∠QNO = ∠QON ✓

NP is a shared edge. ∠MNO = ∠PON as given.

NO is a shared edge. ∠MNO = ∠PON as given. ✓

∴ triangle MNO is congruent to triangle PNO by ASA. ✓

Worksheet

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Lesson Details

Key learning points

By knowing two angles and the length between them 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.

Common misconception

Pupils may struggle to spot congruent triangles when the two angles are not at the ends of the known side.

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.
Similar - Two shapes are similar if the only difference between them is their size. Their side lengths are in the same proportions.