Here,
ABCD is a parallelogram with
AC as its diagonal.
We know, in parallelogram opposites sides are parallel.
So, AB∥DC and AD∥BC
Since, AB∥DC and AC is the transversal
⇒ ∠BAC=∠DCA ---- ( 1 ) [ Alternate angles ]
Similarly, AD∥BC and AC is the transversal.
⇒ ∠DAC=∠BCA ---- ( 2 ) [ Alternate angles ]
Adding ( 1 ) and ( 2 ),
⇒ ∠BAC+∠DAC=∠DCA+∠BCA
⇒ ∠BAD=∠DCB
Similarly, we can prove, ∠ADC=∠ABC
∴ We have proved that, opposite angles of a parallelogram are equal.
![1284564_1427515_ans_4149919e4e7b47a18c5e08b2f24c1560.png](https://search-static.byjusweb.com/question-images/toppr_invalid/questions/1284564_1427515_ans_4149919e4e7b47a18c5e08b2f24c1560.png)