Mary states, if the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle. decide if her statement is true or false?

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.

all the angles opposite to the angle 150 would be 150 and all the angles that are next to 150 are 30 because they equal 180 it you add it up.

step-by-step explanation: