Question

T is a point on the line PS produced of a parallelogram PQRS and QT intersects RS at V. Prove that $△ PQT \sim △ R V Q$ .

Approach

In $△ PQT$ and $△ R V Q$ , $∠ P = ∠ R$ (opposite angles of parallelogram). $∠ T = ∠ V QR$ (alternate interior angles). By AA similarity, $△ PQT \sim △ R V Q$ .

Step-by-step working

1
Correct figure drawn
1 mark
2
$∠ P = ∠ R$ (opposite angles of parallelogram)
1 mark
3
$∠ T = ∠ V QR$ (alternate interior angles). Hence $△ PQT \sim △ R V Q$ by AA.
1 mark

Concepts used

parallelogramsimilarityaa criterion

Approach

Step-by-step working

Concepts used

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