Q1 of 49 Page 45

In the adjoining figure, PQRS is a rectangle. Identify the congruent triangles formed by the diagonals.

In Δ POQ and Δ SOR


OP = OR(Diagonals of a rectangle bisect each other)


OQ = OS(Diagonals of a rectangle bisect each other)


PQ = SR(Diagonals are equal in length)


Δ POQ ≅ Δ SOR by S.S.S. axiom of congruency


In Δ POS and Δ QOR


OP = OR(Diagonals of a rectangle bisect each other)


OQ = OS(Diagonals of a rectangle bisect each other)


PS = QR(Diagonals are equal in length)


Δ POS ≅ Δ QOR by S.S.S. axiom of congruency


In Δ PSQ, Δ PQR, Δ QRS and Δ PRS


PS = QR = QR = PS(Opposite sides of rectangle)


PQ = PQ = SR = SR(Opposite sides of the rectangle)


∠P = ∠Q = ∠R = ∠S (Angles of a rectangle)


Δ PSQ ≅ Δ PQR ≅ Δ QRS ≅ Δ PRS by S.A.S. axiom of congruency


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