Similar shapes

Identify and work with similar and congruent shapes, understanding scale factors and corresponding sides.

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Learning objective overview

Master Teaching Guide coverage for this objective.

Current NZC (2007)
  • GM6-5
New NZC (2026)
  • NZC26-P4-GEO-SHP-K-Y10-01
  • NZC26-P4-GEO-SPR-P-Y10-02

Resources

Terminology

  • similar shapes
  • congruent shapes
  • scale factor
  • corresponding sides
  • corresponding angles
  • enlargement
  • ratio
  • proportional

Task goals

  • Identify whether two shapes are similar or congruent by comparing corresponding sides and angles.
  • Find the scale factor between similar shapes by comparing the lengths of corresponding sides.
  • Calculate missing side lengths in similar shapes using scale factors and proportional reasoning.
  • Understand that corresponding angles in similar shapes are equal, and corresponding sides are in the same ratio.
  • Apply similarity to solve problems involving enlargement and reduction of shapes.

Where this fits

What leads into this objective, and where it goes next.

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Similar shapes

Similar shapes

Know

In similar shapes, corresponding angles are equal and the lengths of corresponding sides are proportional.

Statement▸
Year 10 · Geometry · Shapes
NZC26-P4-GEO-SHP-K-Y10-01
Do

Transforming 2D shapes, including composite shapes, by resizing them by any scale factor

Statement▸
Year 10 · Geometry · Spatial reasoning
NZC26-P4-GEO-SPR-P-Y10-02

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