Question

Which of the following pairs of triangles are congruent? Give reasons
ΔABC;(∠B = 90°,BC = 6cm,AB = 8cm);
ΔPQR;(∠Q = 90°,PQ = 6cm,PR = 10cm).

Answer 1

In ΔABC and ΔPQR
∠B = ∠Q
BC = PQ
By Pythagoras theorem,
PR² = PQ² + QR²
10² = 6² + QR²
100 = 36 + QR²
QR = `sqrt(100 - 36)`
QR = `sqrt(64)` = 8cm
AB = QR
Therefore,
ΔABC ≅ ΔPQR  ...(SAS criteria).