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.

47460698c4110f85e48c318b013792ff.docx

Answer 1

Given:

Quadrilateral ABCD with its each side extended.

AB=AD.

To Find:

To prove that ABCD is a kite.

Solution:

∠BAD=110°

∠C=20°

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

∠CDA=180°-65°=115°

∠B=360-(∠A+∠D+∠C)

∠B=115°

Now in ΔACD and ΔACB

AC=AC (common)

AD=AB(given)

∠CDA=∠CBA(equal)

ΔACD≅ΔACB

CD=CB

AD=AB(adjacent sides are equal)

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

∴ABCD is a kite .