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## Answers

AC= BD (GIVEN, diagonals of parallelogram as equal)

CD= DC ( common)

AD= BC ( opposite sides of a parallelogram are equal)

ΔACD ≡ ( congurent) ΔBDC ( SSS congruence)

So, angle D = angle C ( corresponding parts of congruent triangles)

ANGLE D + ANGLE C = 180 degrees( co- interior angles)

AS, angle D = angle C

180/2 = 90 degrees

As angle D = C = 90 degrees

SO, Angle A = C = 90 degrees ( opposite angles of a parallelogram are equal)

AND, B= D = 90 degrees ( opposite angles of a parallelogram are equal)

ALL ANGLES ARE 90 DEGREES, SO IT IS A RECTANGLE..........

then in ΔABC & ΔBCD

AB=CD

BC= DA

CA=DB

SO,BOTH ARE CONGRUENT BY SSS

SO EACH ANGLE IS EQUAL ,LET ONE ANGLE BEx

⇒4x=360⇒x=90 so it is a rectangle.