Question

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

Answer 1

as  diagonals of a parallelogram divide it into 2 congruent triangles                                  so all the angles will be equal so each angle will be 90*  so it is a rectangle

Answer 2

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..........