Question

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

Answer 1

Answer: The congruent triangles formed by the diagonals are

triangle POQ and triangle ROS

AND

triangle POS and triangle ROQ

Step-by-step explanation:

[tri stands for triangle]

In tri POQ and tri ROS ,

1) PO = RO    (one diagonal of a rectangle bisects the other)

2) QO = SO   (one diagonal of a rectangle bisects the other)

3) angle POQ = angle ROS      (vertically opposite angles)

:. tri POQ ≈ tri ROS    (by SAS axiom of congruency)

Similarly,  tri POS ≈ tri ROQ

           1) PO = RO  ( one diagonal of a rectangle bisects the other)

           2) SO = QO (one diagonal of a rectangle bisects the other)

           3) PS = QR   (opposite sides of a rectangle are equal)

           :. tri POS ≈ tri ROQ    (by SSS axiom of congruency)