Answer:
True
Step-by-step explanation:
Let us consider a parallelogram ABCD in which AB=CD and AD=BC.
Now, from ΔABC and ΔBAD, we have
AD=BC (Opposite sides of parallelogram)
BD=AC (Given)
AB=BA (common)
Thus, by SSS rule of congruency,
ΔABC≅ΔBAD.
Now, by corresponding parts of congruent triangles, we have
∠ABC=∠BAD.
But, we know that ∠ABC and ∠BAD forms the corresponding angle pair, thus ∠ABC+∠BAD=180°
⇒2∠ABC=180
⇒∠ABC=90°
Since they are interior angles of parallel lines AC and BC on the same side of their common secant AB. They are therefore both right, and ABCD is a rectangle.
Hence, the statement If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle is true.
