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In the given figure, ABCD is a quadrilateral in which AB=AD an

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In the given figure, $A BC D$ is a quadrilateral in which $A B = A D$ and $BC = D C$ . Prove that
$A C$ bisects $∠ A$ and $∠ C$ .

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Chloe Discussed

In the given figure,

A BC D

is a quadrilateral in which

A B = A D

and

BC = D C

. Prove that

A C

bisects

∠ A

and

∠ C

13 mins ago

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13 mins ago

Text solutionVerified

Consider

△ A BC

and

△ A D C

It is given that

A B = A D

and

BC = D C

A C

is common ie.,

A C = A C

By SSS congruence criterion

△ A BC ≅ △ A D C .... (i)

∠ B A C = ∠ D A C

so we get

∠ B A E = ∠ D A E

We know that

A C

bisects the

∠ B A D

ie.,

∠ C

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Question Text	In the given figure, $A BC D$ is a quadrilateral in which $A B = A D$ and $BC = D C$ . Prove that $A C$ bisects $∠ A$ and $∠ C$ .
Answer Type	Text solution:1
Upvotes	150

In the given figure, ABCD is a quadrilateral in which AB=AD and BC=DC. Prove thatAC bisects ∠A and ∠C.

Text solutionVerified

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In the given figure, $A BC D$ is a quadrilateral in which $A B = A D$ and $BC = D C$ . Prove that
$A C$ bisects $∠ A$ and $∠ C$ .