Using similarity to prove relations
Once two triangles are proved similar, you can use corresponding side ratios and equal angles to prove lengths, proportions, and parallel-line results.
Practice This ConceptMain explanation
Teacher explanation
Similarity is not only a naming result. It becomes a tool for proving unknown lengths, ratios, and geometric relations inside a figure.
Example
If triangles ABC and DEF are similar, then AB/DE = BC/EF = AC/DF can be used to find a missing side or check a proportion.
Simple analogy
Prove similarity once, then ratios do the rest.
Common confusion
Students often stop after writing the similarity statement and do not use the corresponding side ratios.
Exam tip
After proving similarity, write only matching side ratios and keep the vertex order correct.
Answer writing and exam use
1-mark use
Write the exact meaning of using similarity to prove relations in one clean line.
2-mark use
Define using similarity to prove relations and add one example or condition.
3-mark use
Explain using similarity to prove relations, show the method or example, and mention the common mistake.
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