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Summary Congruence-and-Similarity.docx
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edexcel Gcse maths math mathematics summary document definitions with examples
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Topic/SkillTopic: Definition/Tips
Congruence and Similarity Example
1. Congruent Shapes are congruent if they are identical -
Shapes same shape and same size.
Shapes can be rotated or reflected but still
be congruent.
2. Congruent 4 ways of proving that two triangles are
Triangles congruent:
1. SSS (Side, Side, Side)
2. RHS (Right angle, Hypotenuse, Side)
3. SAS (Side, Angle, Side)
4. ASA (Angle, Side, Angle) or AAS
ASS does not prove congruency.
3. Similar Shapes are similar if they are the same
Shapes shape but different sizes.
The proportion of the matching sides must
be the same, meaning the ratios of
corresponding sides are all equal.
4. Scale Factor The ratio of corresponding sides of two
similar shapes.
To find a scale factor, divide a length on
one shape by the corresponding length on
a similar shape.
Scale Factor = 15 ÷10=1.5
5. Finding 1. Find the scale factor.
missing 2. Multiply or divide the corresponding
lengths in side to find a missing length.
similar shapes
If you are finding a missing length on the
larger shape you will need to multiply by
the scale factor.
If you are finding a missing length on the
smaller shape you will need to divide by Scale Factor = 3 ÷ 2=1.5
the scale factor. x=4.5× 1.5=6.75 cm
6. Similar To show that two triangles are similar,
Triangles show that:
1. The three sides are in the same
proportion
2. Two sides are in the same proportion,
and their included angle is the same
3. The three angles are equal
Mr A. Coleman Glyn School
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