Question

In a quadrilateral ABCD, AD and BD are the bisectors of angle A and angle B.Prove that angle ABD = 1/2 (angle C + angle B)

Answer 1

Step-by-step explanation:

ABCD is a quadrilateral

To prove : ∠AOB=

2

1

(∠C+∠D)

AO and BO is bisector of A and B

∠1=∠2∠3=∠4...(1)

∠A+∠B+∠C+∠D=360

(Angle sum property)

2

1

(∠A+∠B+∠C+∠D)=180...(2)

In △AOB

∠1+∠3+∠5=

2

1

(∠A+∠B+∠C+∠D)

∠1+∠3+∠5=∠1+∠3+

2

1

(∠C+∠D)

∠AOB=

2

1

(∠C+∠D)

Hence,Proved.

Answer 2

Answer:

ABCD is a quadrilateral

To prove : ∠ADB=

2

1

​

(∠C+∠D)

AD and BD is bisector of A and B

∠1=∠2∠3=∠4...(1)

∠A+∠B+∠C+∠D=360

(Angle sum property)

2

1

​

(∠A+∠B+∠C+∠D)=180...(2)

In △ADB

∠1+∠3+∠5=

2

1

​

(∠A+∠B+∠C+∠D)

∠1+∠3+∠5=∠1+∠3+

2

1

​

(∠C+∠D)

∠ADB=

2

1

​

(∠C+∠D)

​

Hence,Proved