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The diagram below shows two right-angled triangles - OCR - GCSE Maths - Question 12 - 2018 - Paper 1

Question 12

The diagram below shows two right-angled triangles. Prove that triangles PQS and QRS are similar.

Worked Solution & Example Answer:The diagram below shows two right-angled triangles - OCR - GCSE Maths - Question 12 - 2018 - Paper 1

Step 1

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Answer

Since both triangles PQS and QRS share the angle at point Q, we have:

$\angle PQS = \angle QRS$

This gives us one pair of equal angles.

Step 2

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Answer

We can use the fact that both triangles are right-angled triangles at points Q and R:

$\angle PSQ = \angle QSR = 90^\circ$

This provides another pair of equal angles.

Step 3

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Answer

By the Angle-Angle (AA) similarity criterion, since we have two pairs of corresponding angles that are equal, triangles PQS and QRS are similar:

$\triangle PQS \sim \triangle QRS$

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