In the given figure, TQ = SR, PT = 4 cm, and SR = 6 cm. Find the measure of TS.

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Solution

In the triangles, $△$ TPQ and $△$ SRQ,
$∠$ PTQ = $∠$ QSR = right angle
side TS = side SR (given)
$∠$ TQP = $∠$ SRQ (given in figure)

Hence, $△$ TQP $≅ △$ SRQ by ASA criterion for congruency of triangles.

$∴$ TQ = SR = 6 cm
and, QS = PT = 4 cm

So, TS = TQ - QS = 6 - 4 = 2 cm

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