Question

prove that bisector of alternate interior angles are equal​

Answer 1

Answer:

Given: AB and CD are the bisector of ∠PAC and ∠RCA,AB∥CD

Since AB and CD are angles bisectors

So, ∠DCR=∠DCA=α and ∠PAB=∠CAB=β

Now, AB∥CD

∠BAC=∠DCA

β=α

Since, alternate angles are equal

Thus, PQ∥RS

Answer 2

Answer:

Given: AB and CD are the bisector of ∠PAC and ∠RCA,AB∥CD

Since AB and CD are angles bisectors

So, ∠DCR=∠DCA=α and ∠PAB=∠CAB=β

Now, AB∥CD

∠BAC=∠DCA

β=α

Since, alternate angles are equal

Thus, PQ∥RS