Question

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

Answer 1

In $△POQ$ and $△SOR$

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

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

$PQ=SR$(Diagonals are equal in length)

$△POQ\cong △SOR$ by S.S.S. axiom of congruency

In $△POS$ and $△QOR$

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

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

$PS=QR$(Diagonals are equal in length)

$△POS\cong △QOR$ by S.S.S. axiom of congruency

In $△PSQ$, $△PQR$,$△QRS$ and $△PRS$

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

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

$\angle P=\angle Q=\angle R=\angle S$(Angles of a rectangle)

$△PSQ\cong △PQR\cong △QRS\cong △PRS$ by S.A.S. axiom of congruency