Question

show that abcd is a kite. Give a reason for each stage of your working

Answer 1

Answer:

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)