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T is a point on the line PS produced of a parallelogram PQRS and QT intersects RS at V. Prove that $\triangle PQT \sim \triangle RVQ$.
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Solution:
In $\triangle PQT$ and $\triangle RVQ$
$\angle P = \angle R$ (opposite angles of a parallelogram) (1 Mark)
$\angle T = \angle VQR$ (alternate interior angles) (1 Mark)
$\triangle PQT \sim \triangle RVQ$ (By AA similarity criterion) (1 Mark)
In $\triangle PQT$ and $\triangle RVQ$
$\angle P = \angle R$ (opposite angles of a parallelogram) (1 Mark)
$\angle T = \angle VQR$ (alternate interior angles) (1 Mark)
$\triangle PQT \sim \triangle RVQ$ (By AA similarity criterion) (1 Mark)