Shape and Space 5
3 marks · HardExplain how you would distinguish between congruent and similar triangles on a coordinate grid. Give examples of a transformation that produces congruent triangles and one that produces similar triangles.
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Must show: Definition of congruence: shapes exactly the same size and shape, matching lengths and angles, Definition of similarity: shapes same shape but different sizes, angles equal but side lengths in same ratio, Example of congruence: translation, rotation, reflection, Example of similarity: enlargement by scale factor other than 1
Common mistakes: Confusing congruent and similar; Suggesting enlargement produces congruence
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Marking points
B1 · 1 mark · Correct explanation of congruence (all sides and angles equal: identical in shape and size)
B2 · 1 mark · Correct explanation of similarity (angles equal, sides in same ratio: same shape, not necessarily same size)
B3 · 1 mark · Clear example of each: a transformation producing congruence (e.g., reflection), and one producing similarity (e.g., enlargement)
Worked solution
Congruent triangles have exactly the same size and shape; all sides and angles are equal. To identify congruence on a coordinate grid, check that all corresponding sides are equal in length and all angles are equal (for example, under translation, rotation, or reflection).
Similar triangles have the same shape but can be different sizes. Their corresponding angles are equal, but their sides are in the same ratio (for example, under enlargement).
For example, a reflection in any line or a translation by a vector produces a congruent triangle, as the size and shape are preserved. On the other hand, an enlargement with a scale factor different from 1 produces a similar triangle (not congruent), as the angles are preserved but the sides are multiplied by the scale factor.