Congruent shapes and matching parts | Year 8

01 / LEARN

The idea, step by step

Same shape and same size

Congruent shapes can fit exactly on top of one another. Sliding, turning or reflecting one shape may be necessary. None of these movements changes a side length or an angle. Enlargement scale factors in this chapter are positive. A scale factor other than 1 changes size, so it does not produce congruent shapes.

Corresponding parts are the parts that match. In the diagram, A matches D, B matches E and C matches F. Their matching side lengths are equal even though one triangle is flipped.

Read the order carefully

The statement $△ A B C ≅ △ D E F$ records three pairings in order: A with D, B with E and C with F. Therefore AB matches DE, BC matches EF and AC matches DF.

Write the pairings before calculating a missing side or angle. An angle named ABC has vertex B, so it matches angle DEF, whose middle letter is E. A drawing’s orientation is not a reliable guide to the correspondence.

A common trap

Assuming that the side drawn at the bottom always matches the bottom side of the other shape.

Instead: Use the stated vertex correspondence or marked equal parts; shapes may be turned or reflected.

02 / WORKED EXAMPLES

See the thinking

Example 1

Use matching sides

Given $△ A B C ≅ △ P Q R$ , AB = 6 cm and BC = 8 cm. Find PQ and QR.

The stated order pairs A with P, B with Q and C with R.
AB corresponds to PQ, so PQ = 6 cm.
BC corresponds to QR, so QR = 8 cm.

PQ = 6 cm; QR = 8 cm.

Example 2

Use matching angles

Given $△ A B C ≅ △ X Y Z$ , angle A is 50° and angle B is 60°. Find angles Y and Z.

B corresponds to Y, so angle Y is 60°.
Angle C is $180 - 50 - 60 = 70$ °.
C corresponds to Z, so angle Z is 70°.

Y = 60°; Z = 70°.

Check your understanding

If $△ K L M ≅ △ R S T$ , which side matches LM?

Show answer

ST.

L pairs with S and M pairs with T.

03 / WORKSHEET

Your turn

6 questions · 11 marks · Work at your own pace.

Worksheet PDF Worked solutions

Read the questions online

If $△ A B C ≅ △ D E F$ , name the angle corresponding to angle B.
1 mark
If $△ A B C ≅ △ P Q R$ , name the side corresponding to AC.
1 mark
Given $△ A B C ≅ △ X Y Z$ and BC = 9 cm, find YZ.
2 marks
Two congruent triangles have corresponding angle measures $3 x$ degrees and 72°. Find $x$ .
2 marks
Given $△ D E F ≅ △ L M N$ , angle D = 42° and angle E = 78°. Find angle N.
3 marks
A shape is reflected in a mirror line. Explain why its image is congruent to the original.
2 marks

Read the worked solutions

Equivalent correct methods earn the corresponding marks. Include units where asked.

If $△ A B C ≅ △ D E F$ , name the angle corresponding to angle B.
1 mark
The second vertices B and E correspond.
Angle E.
If $△ A B C ≅ △ P Q R$ , name the side corresponding to AC.
1 mark
A pairs with P and C pairs with R.
PR.
Given $△ A B C ≅ △ X Y Z$ and BC = 9 cm, find YZ.
2 marks
BC and YZ are corresponding sides, so their lengths are equal.
9 cm.
Two congruent triangles have corresponding angle measures $3 x$ degrees and 72°. Find $x$ .
2 marks
$3 x = 72$ , so $x = 72 / 3 = 24$ .
$x = 24$ .
Given $△ D E F ≅ △ L M N$ , angle D = 42° and angle E = 78°. Find angle N.
3 marks
Angle F is $180 - 42 - 78 = 60$ °.
F corresponds to N.
60°.
A shape is reflected in a mirror line. Explain why its image is congruent to the original.
2 marks
A reflection reverses orientation but does not stretch or shrink the shape.
Reflection preserves every side length and angle, so the shape and size remain unchanged.

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Curriculum reference & lesson scope

Australian Curriculum v9 / SA Curriculum

Congruent shapes and matching parts; triangle congruence tests; similar shapes and corresponding sides; triangle similarity; properties of quadrilaterals established using triangles; testing congruence/similarity with transformations; decision-tree algorithms and digital geometry.

Official curriculum source ↗

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