Congruence and similarity · Grade 9
In Grade 9 you learn: similar shapes and scale factors.
Congruent shapes are identical in shape and size. Similar shapes have the same shape but may be different sizes: all their lengths are in the same ratio (the scale factor), and their angles are equal.
Key facts
- Triangles are congruent if they match by SSS, SAS, ASA (or AAS) or RHS. AAA is not enough.
- Similar shapes: length scale factor k = new length ÷ old length.
- Equal angles (from parallel lines or vertically opposite angles) often show that triangles are similar.
Worked examples
Example 1
The triangles are similar. Find x.
Answer: x = 10 cm