Pawan Prajapati
Last Activity: 3 Years ago
Consider triangles DAB and CBA,
AD = BC [Opposite sides of a parallelogram]
AB is common.
AC = BD
:. Ii DAB ::Ii CBA
=> L DAB = L CBA
[Given]
[ss.sJ
DC
A B
••.(i) [CPCT)
As ABCD is a parallelogram. AD II BC and AB is transversal.
.. L DAB + L CBA = 180° [Sum of interior angles on
the same side of transversal is 180°.)
=> 2L DAB = 180° [From (i)]
=> L DAB = 90°
As in a parallelogram, LDAB = 90°. Hence, the parallelogram is a rectangle.