GCSE Maths Practice: congruence-and-similarity

Question 8 of 10

This question asks which conditions are sufficient to prove triangle similarity. Recognising similarity is key in GCSE geometry.

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\( \begin{array}{l}\text{Which conditions prove triangle similarity?}\end{array} \)

Select all correct options:

AAA, SSS in proportion, SAS in proportion prove similarity. SSA does not.

Triangle similarity means shapes have the same angles and their sides are in proportion. AAA ensures all angles match, so triangles are similar, though side lengths may differ. SSS in proportion checks that corresponding sides have the same ratio, and SAS in proportion checks that two sides and the included angle are proportional. SSA does not guarantee similarity because the angle may not be included between the sides, leading to ambiguity. Understanding these rules helps in solving proportionality problems, scaling triangles, and interpreting geometric diagrams. Applying these criteria consistently allows students to find missing lengths, solve ratio problems, and prove similarity in diagrams and real-world applications. Practising these concepts develops visual reasoning and strengthens problem-solving skills for GCSE geometry.