01 Key Concepts
Similar Figures
Figures with the same shape: corresponding angles are equal, and corresponding sides are in proportion (the same ratio).
Scale Factor
The ratio between corresponding side lengths of two similar figures, describing how much bigger or smaller one is than the other.
AA Similarity (Angle-Angle)
If two angles of one triangle equal two angles of another, the triangles are similar (the third angles must also match, since angles sum to 180°).
Using Proportions to Find Missing Sides
Set up a ratio between corresponding sides of similar figures and solve for the unknown length.
Similarity vs. Congruence
Congruent figures are always similar (scale factor of 1), but similar figures are only congruent if their scale factor equals 1.
02 Key Formulas
- Scale factor = (side of figure 2) / (corresponding side of figure 1)
03 Solved Examples
Example 1 Triangle ABC has sides 3, 4, 5. Triangle DEF is similar with a scale factor of 2. Find the sides of DEF.
- Multiply each side of ABC by the scale factor 2.
- 3*2=6, 4*2=8, 5*2=10.
Answer: DEF has sides 6, 8, 10
Example 2 Two similar triangles have corresponding sides 4 and 10. Find the scale factor.
- Scale factor = 10/4.
Answer: Scale factor = 2.5
Example 3 Two similar triangles have corresponding sides 6 and 9. If a side in the smaller triangle is 8, find the corresponding side in the larger triangle.
- Find the scale factor: 9/6 = 1.5.
- Multiply the given side by the scale factor: 8*1.5.
Answer: 12
04 Practice Questions
1Triangle ABC has sides 2,3,4. Triangle similar with scale factor 3. Find its sides.
6, 9, 12
2Two similar triangles have corresponding sides 5 and 15. Find the scale factor.
3
3What rule says two triangles are similar if two angles match?
AA similarity
4Are all congruent figures also similar?
Yes
5Are all similar figures also congruent?
No, only if the scale factor is exactly 1
📄 Similarity — Downloadable Worksheet
10 questions with a full answer key. Grab the PDF to print, or try the interactive version in your browser.