Question

6. Diagonal AC of a parallelogram ABCD bisects A. Show that
(1) it bisects angle C also.
(ii) ABCD is a rhombus.

Please give write answer.
I will mark as brainlist.​

Answer 1

Given: A parallelogram ABCD in which diagonal AC bisect angle A

To Prove: Diagonal AC bisects angle C

ABCD is a rhombus

Proof: Angle DAC=angle BCA. (alternate angle)

Angle BAC=angle DCA. (alternate angle)

but,angleDAC =angle BAC. (given)

angleBCA =angleDCA

Hence AC bisect angle C

in triangle ABC and CDA

AC. = AC (Common)

angleBAC=angleDAC. (Given)

angle BAC=angleDAC. (Proved)

triangle ABC congruent triangle ADC. (ASA)

BC=DC (CPCT)

but,. AB =DC (given)

AB= DC= DC=AD

ABCD is a rhombus

Hence Proved