AI generatedGeometry and measuresKey Stage 3

Recognising similar shapes

Recognising similar shapes.

  • Match corresponding lengths before taking a ratio.
  • Length scale factor gives area factor and volume factor .
  • Reverse with a square root or cube root when an area or volume ratio is given.

Example 1

The triangles have the same corresponding angles. Check whether the shown sides are in the same ratio.

Two triangles with equal corresponding angles, not to scaleEqual corresponding angles; not to scale
First ratioCompare corresponding sides in the same direction.
Second ratioBoth ratios are equal and corresponding angles are equal.
The triangles are similar, with length scale factor .

Example 2

The triangles have the same corresponding angles. Check whether the shown sides are in the same ratio.

Two triangles with equal corresponding angles, not to scaleEqual corresponding angles; not to scale
First ratioCompare corresponding sides in the same direction.
Second ratioBoth ratios are equal and corresponding angles are equal.
The triangles are similar, with length scale factor .

Your turn

Question 1

The triangles have the same corresponding angles. Check whether the shown sides are in the same ratio.

Two triangles with equal corresponding angles, not to scaleEqual corresponding angles; not to scale
Check answer
First ratioCompare corresponding sides in the same direction.
Second ratioBoth ratios are equal and corresponding angles are equal.
The triangles are similar, with length scale factor .
Question 2

The triangles have the same corresponding angles. Check whether the shown sides are in the same ratio.

Two triangles with equal corresponding angles, not to scaleEqual corresponding angles; not to scale
Check answer
First ratioCompare corresponding sides in the same direction.
Second ratioBoth ratios are equal and corresponding angles are equal.
The triangles are similar, with length scale factor .
Question 3

The triangles have the same corresponding angles. Check whether the shown sides are in the same ratio.

Two triangles with equal corresponding angles, not to scaleEqual corresponding angles; not to scale
Check answer
First ratioCompare corresponding sides in the same direction.
Second ratioBoth ratios are equal and corresponding angles are equal.
The triangles are similar, with length scale factor .
Question 4

The triangles have the same corresponding angles. Check whether the shown sides are in the same ratio.

Two triangles with equal corresponding angles, not to scaleEqual corresponding angles; not to scale
Check answer
First ratioCompare corresponding sides in the same direction.
Second ratioBoth ratios are equal and corresponding angles are equal.
The triangles are similar, with length scale factor .
Question 5

The triangles have the same corresponding angles. Check whether the shown sides are in the same ratio.

Two triangles with equal corresponding angles, not to scaleEqual corresponding angles; not to scale
Check answer
First ratioCompare corresponding sides in the same direction.
Second ratioBoth ratios are equal and corresponding angles are equal.
The triangles are similar, with length scale factor .
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