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Maths

Congruent and similar shapes

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# Congruent shapes

If two shapes are congruent, they are identical in both shape and size.

Remember: Shapes can be congruent even if one of them has been rotated or reflected.

Question

Which of the shapes in the illustration above are congruent?

Did you get the following pairs?

• A and G
• D and I
• E and J
• C and H

Remember: Shapes can be congruent even if one of them has been rotated (as in A and G) or reflected (as in C and H).

The symbol means 'is congruent to'.

Two triangles are congruent if one of the following conditions applies:

## 1. Three sides are the same

The three sides of the first triangle are equal to the three sides of the second triangle (the SSS rule: Side Side Side).

## 2. Two sides and one angle are the same

Two sides of the first triangle are equal to two sides of the second triangle, and the included angle is equal (the SAS rule: Side Angle Side).

## 3. Two angles and one side are the same

Two angles in the first triangle are equal to two angles in the second triangle, and one (similarly located) side is equal (the AAS rule: Angle Angle Side).

## 4. Two sides in right-angled triangle are the same

In a right-angled triangle, the hypotenuse and one other side in the first triangle are equal to the hypotenuse and corresponding side in the second triangle (the RHS rule: Right-angled, Hypotenuse, Side).

Question

For each of the following pairs of triangles, state whether they are congruent. If they are, give a reason for your answer (SSS, SAS, AAS or RHS).

Pair 1

Pair 2

Pair 3

1. Yes. RHS
2. Yes. SSS
3. No. The side of length 7cm is not in the same position on both triangles. Therefore, it is not AAS.

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