CAIE IGCSE Mathematics Similarity Problems and Proofs

Practise proving triangles similar from angle facts, distinguishing congruence from similarity and using scale factors in linked geometry problems.

Exam points

state two equal angle pairs with geometrical reasons before concluding that triangles are similar
distinguish congruent figures as the same size and shape from similar figures with a scale factor
use corresponding sides from the proven similar triangles before applying further geometry

[Maximum number: 3]

NOT TO SCALE

In the diagram, S lies on PQ and T lies on PR.
ST is parallel to QR.

Explain why triangle PQR is mathematically similar to triangle PST.

Give a geometrical reason for each statement you make.

Three correct pairs with correct reasons

$\angle PQR=\angle PST$ and corresponding angles
$\angle PRQ=\angle PTS$ and corresponding angles
$\angle QPR=\angle TPS$ and common angle
OR
Two correct pairs with correct reasons and correct similarity condition, e.g. AAA

B2 for two correct pairs with correct reasons
or B1 for one correct pair with correct reason

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E4.4.3 Solve problems and give simple explanations involving similarity question 1