Question

6. In the adjoining diagram, ABCD is a par-
allelogram in which AB > AD. Prove that
< BAC < DAC.​

Answer 1

as AB>AB

then construct a diagonal AC joining A and C

now we get 2 triangles

proof: In triangles ABC and ADC

AB=DC (given)

BC=AD(given)

AC=AC(common)

hence, triangles ABC and ADC are congruent (by was congruence rule)

now,

angles ACB and DAC are equal (cpct).........(i)

angles ACD and BAC are equal (cpct).........(ii)

thus, the sum of angles DAC and BAC = the sum of angles ACB and ACD (from eq i, ii).....(iii)

therefore, angle DAB and BCD are equal (from eq iii)

Hence proved