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Angle Bisector

ABCD is a kit...

Question

ABCD is a kite, then which of these statements are correct?

A

Congruent triangles are formed.

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B

Angle formed at point B corresponds to angle formed at point D.

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C

Non congruent triangles are formed.

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D

∠ B A C = ∠ D C A

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Solution

The correct options are
A Congruent triangles are formed.
B Angle formed at point B corresponds to angle formed at point D.
For a kite as labelled above,
side AB = side AD
and side BC = side DC

In $△ A B C$ and $△ A D C$ ,
CA = CA .... (Common side)
AB = AD .... (ABCD is a Kite)
BC = DC .... (ABCD is a Kite)

Therefore, $△ A B C ≅ △ A D C$
by SSS criterion for congruency of triangles.

Hence, angle formed at B corresponds to angle formed at D.

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