Congruence and similarity.
Identify matching geometric parts, justify congruence and similarity, then apply transformations and proof to solve problems.
Work through the topic
Learn the method, follow the examples, then try the worksheet.
- 01
Congruent shapes and matching parts
Match corresponding vertices, sides and angles before using congruence information.
- 02
Triangle congruence tests
Choose sufficient side and angle information to prove two triangles congruent.
- 03
Similar shapes and corresponding sides
Use corresponding-side ratios to calculate missing lengths in similar figures.
- 04
Triangle similarity
Prove triangle similarity, then use a correct correspondence to solve a length problem.
- 05
Properties of quadrilaterals established using triangles
Use congruent triangles to explain familiar quadrilateral properties rather than relying on appearance.
- 06
Testing congruence/similarity with transformations
Use coordinate transformations to test whether an image preserves size or changes it proportionally.
- 07
Decision-tree algorithms and digital geometry
Design a reliable sequence of geometric checks, and distinguish a digital test from a proof.
Topic review
Revisit the key ideas, then choose a practice paper.