Question

In the quadrilateral ABCD, AC = DC, ∠B = 82°, ∠ACB = 30°. Show that DC > AB and DC > BC.

Answer 1

Given,

ABCD is a quadrilateral, AC = DC, ∠B = 82°, ∠ACB = 30°.

We need to show that DC > AB and DC > BC.

In ΔABC, ∠BAC + ∠ACB + ∠B = 180°   ...(Angle sum property of triangle)

∠BAC + 30° + 82° = 180°

∠BAC = 68°

In ΔABC, ∠ABC > ∠ACB   ...(The side opposite to the largest angle is the longest in triangles.)

AC > AB  ...(1)

Similarly, ∠ABC > ∠BAC   ...(The side opposite to the largest angle is the longest in triangles.)

AC > BC  ...(2)

As AC = DC, substituting in equation (1) and (2),

So, DC > AB and DC > BC

Hence, proved.