Prove that if one pair of opposite sides of a quadrilateral is equal and parallel, it is a parallelogram

Asked by mkp400 | 18th Dec, 2017, 07:52: AM

Expert Answer:

begin mathsize 16px style In space quadrilateral space ABCD comma
AB equals CD space and space AB space parallel to space CD
Join space AC
AC space is space transversal.
angle DCA space equals space angle BAC space space space space space space Alternate space angles
In space increment DCA space and space increment BAC
DC equals AB space space space space space space space space space space space space space space space space space space space space space given
angle DCA equals angle BAC
AC space equals space AC space space space space space space space space space space space space space space space space space space Common space side
increment DCA space approximately equal to space increment BAC space space space space SAS
angle DAC equals angle BCA space space space space space space space space space space space space space space space space space
Similarly space you space can space prove space DA parallel to CB
Hence comma space ABCD space is space straight a space parallelogram. end style

Answered by Sneha shidid | 18th Dec, 2017, 09:57: AM