Congruent shapes and matching parts | Year 8

01 / LEARN

Understand the idea.

Same shape and same size

Congruent shapes have the same shape and size: one can cover the other exactly after a slide, turn or reflection. These movements preserve every length and angle, even when the image points in a different direction.

Identify the corresponding parts before comparing measurements. In the diagram, $A$ matches $D$ , $B$ matches $E$ and $C$ matches $F$ . The flipped appearance does not alter those pairings or the equality of matching lengths.

Read the order carefully

The vertex order in $△ A B C ≅ △ D E F$ records the correspondence: $A \leftrightarrow D$ , $B \leftrightarrow E$ , $C \leftrightarrow F$ . Match both endpoints to pair sides, giving $A B \leftrightarrow D E$ , $B C \leftrightarrow E F$ and $A C \leftrightarrow D F$ .

For angles, the middle letter identifies the vertex: $∠ A B C$ is at $B$ , so it matches $∠ D E F$ at $E$ . Once a pair is identified, congruence lets you set its measurements equal. Never match parts just by their position on the page.

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Use matching sides

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

Worked solution

1
Read the matching vertices from the order.
$A \leftrightarrow P, B \leftrightarrow Q, C \leftrightarrow R$
The congruence statement gives the correspondence in order.
2
Match the side with endpoints A and B.
$P Q = A B = 6 cm$
A matches P and B matches Q, so these sides correspond.
3
Match the side with endpoints B and C.
$Q R = B C = 8 cm$
Corresponding sides of congruent triangles have equal lengths.

Answer

PQ = 6 cm; QR = 8 cm.

EXAMPLE 02

Use matching angles

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

Worked solution

1
Match the angle at B.
$∠ Y = ∠ B = 60^{\circ}$
The stated order pairs B with Y.
2
Find the remaining angle in ABC.
$∠ C = 180^{\circ} - 50^{\circ} - 60^{\circ} = 70^{\circ}$
The three interior angles of a triangle sum to 180 degrees.
3
Match the angle at C.
$∠ Z = ∠ C = 70^{\circ}$
C corresponds to Z, so congruence transfers the angle.

Answer

Y = 60°; Z = 70°.

03 / YOUR TURN

Try it yourself.

Check your understanding

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

Show answer & reasoning

ST.

In $△ K L M ≅ △ R S T$ , $L$ matches $S$ and $M$ matches $T$ . Therefore the side joining $L$ to $M$ matches $S T$ .

Keep practising

6 worksheet questions · 11 marks

Open worksheet 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 $A C$ .
1 mark
Given $△ A B C ≅ △ X Y Z$ and $B C = 9$ cm, find $Y Z$ .
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 $A C$ .
1 mark
$A$ pairs with $P$ and $C$ pairs with $R$ .
$P R$ .
Given $△ A B C ≅ △ X Y Z$ and $B C = 9$ cm, find $Y Z$ .
2 marks
$B C$ and $Y Z$ 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 $x = \frac{72}{3} = 24$ .
$x = 24$ .
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 ↗

In this lesson

Understand the idea.

Same shape and same size

Read the order carefully

See the method in action.

Use matching sides

Read the matching vertices from the order.

Match the side with endpoints A and B.

Match the side with endpoints B and C.

Use matching angles

Match the angle at B.

Find the remaining angle in ABC.

Match the angle at C.

Try it yourself.

Check your understanding

Keep practising