Q6 of 33 Page 95

If in the parallelogram ABCD, AB > AD, then I prove with reason that ∠BAC < ∠DAC.

Given: Parallelogram ABCD


AB > AD


Construction:- Join AC which is the diagonal of Parallelogram


AB = CD and AD = BC


In Δ ABD


AB >AD


⇒ CD > AD


Now, if two sides of a triangle are unequal, the angle opposite to the longer side is larger


Hence ∠DAC > ∠ACD ………1


But ∠ACD = ∠BAC (alternate angles)


⇒ ∠DAC > ∠BAC


Hence proved.


More from this chapter

All 33 →
4

By calculating, I write the values of X and Y in the following rectangle PQRS:

 5

In the figure aside, ABCD and ABEF are two parallelograms. I prove with reason that CDFE is also a parallelogram.

 1

Firoz has drawn a quadrilateral PQRS whose side PQ = SR and PQ || SR; I prove with reason that PQRS is a parallelogram.

 2

Sabba has drawn two straight line segments AD and BC such that, AD || BC and AD = BC; I prove with reason that AB = DC and AB || DC.