Question

Abcd is a quadrilatetal in which ab=cd and ad=bc .Show that it is s parallelogram. Hint:-draw one of the diagonals.

Answer 1

Given: ABCD is a quadrilateral
AB=CD
AD=BC
To show: ABCD is a parallelogram
construction : join AC
solution : in triangle ADC and triangle ABC
AB=CD (given)
AD=BC (given)
AC=AC (common)
-> triangle ADC = triangle ABC (by SSS)
->angle DAC=angle BCA (by CPCT) .........1
-> angle BAC = angle DCA ( by CPCT) ............2
adding 1 and 2
angle DAC + angle BAC = angle BCA + angle DCA
angle A = angle C
These are opposite angles
-> ABCD is a parallelogram opposite angles are equal
hence proved