Question

In a parallelogram ABCD, AC bisect the angle A. show that ABCD is a

rhombus.

​

Answer 1

Step-by-step explanation:

Given-:AC bisects angle A.

Then <BAC=<DAC.

To prove -: ABCD is a rhombus.

Prove-: <BAC=<DAC(Given).-: (I)

AD||BC (opposite sides of a llgram are equal and parallel).

Then,

<DAC=<BCA.-:(ii)

From eqn I and ii

<BAC=<BCA-:(iii)

=>BC=AB(Sides opposite to equal angles of a triangle are equal).

Similarly we can prove that AD=DC.

Then,

AB=BC=CD=DA.

A llgram with adjacent sides equal is a rhombus.

Hence ABCD is a rhombus.