Question

If the diagonals of a parallelogram are equal, show that is a rectangle

Answer 1

In ΔACD and ΔBDC
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.......... 

Answer 2

let ABCD be a llgram
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.