Similarity problems
Objective. Combine ratio, algebra and geometry in multi-step solutions.
- 1. Learn
- 2. Worked example
- 3. Practice
- 4. Feedback
- 5. Continue
Learn: the key idea
Similarity problems develops a connected mathematical idea rather than an isolated trick. Use invariant properties and scale factors in geometric reasoning. Begin by representing the quantities or relationships, choose a rule that fits, justify each transformation, and finish by checking units, signs, scale and whether the answer is reasonable.
Worked example
Similar shapes have corresponding sides 9 and 18. Find the scale factor.
- 1Identify the known information, the unknown and any conditions.
- 2Choose a diagram, table, graph or algebraic representation that exposes the structure.
- 3Apply the relevant rule one justified step at a time, keeping exact values where useful.
- 4Check by substitution, inverse reasoning or estimation. The result is 2.
Answer: 2
Concept mastery
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Practice
Practice happens on its own screen, one question at a time. Answers stay hidden until you submit yours, and you can stop and pick up at the same question later.
Start practisingCommon mistake. A common error in similarity problems is to copy a procedure without checking its conditions. Label the structure first and justify every sign, operation and unit.
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