Question

The diagram shows a quadrilateral ABCD with each of its sides extended. ab=ad show that abcd is a kite give a reason for each stage of your working.

Answer 1

Answer:

The rest of the question is the attached figure.

Construct the line segment AC

As shown at the graph:

∠BAD = 110°  and ∠C = 20°

∴∠BCD = 20° (Vertically opposite angles).

∠CDA = 180°-65° = 115°

∠B = 360 - (∠A+∠D+∠C) = 360 - (110 + 115 + 20) = 115°

Now in ΔACB and ΔACD

AC = AC (common)

AB = AD (given)

∠CBA =∠CDA (proved)

ΔACB ≅ ΔACD

∵ CPCTC  ⇒ ∴ CB = CD

So, AD = AB and CB = CD (adjacent sides are equal)

∠D =∠B (A pair of opposite angles equal)

∴ ABCD is a kite .