Question

Answer Plzzz............​

Answer 1

Refer to The Attachment.

Answer 2

$\huge\underbrace\mathbf\pink{Answer}$

Given :-

• AB = AD

• CB = CD

Solution :-

⇒Let ABCD be a quadrilateral where AB=AD and CB=CD.

⇒Consider triangle ADB , as AB=AD, it is an isosceles triangle.

We know that,

⇒Property of isosceles triangle , angle ADB = angle ABD

∴ Triangle ADB is similar to triangle ABD.

Now of similar triangle => side OD = side OB.

⇒ AB/OB = AD/OD

⇒ AO is a bisector of BD.

Similarly, in triangle BCD, BC= CD

⇒It is also isosceles triangle , therefore angle CDB=angle CBD.

⇒Hence , Triangle CDB is similar to triangle CBD.

⇨Side OB= side OD.

⇨CD/OD = CB/OB

⇨CO is a bisector of BD.

As OA and OC is the bisector of triangle ABD and triangle BCD respectively.

∴ AC is a bisector of BD and perpendicular to BD.

Hence Proved