A quadrilateral is parallelogram if its opposite angles are equal.

Explanation

Given: A quadrilateral `ABCD` in which opposite angles are equal i.e.,
`/_A=/_C` and `/_B=/_D`
To prove: `ABCD` is a parallelogram i.e,
`AB` parallel to `DC` and `AD` parallel to `BC`.
Proof:
Since, the sum of the angles of quadrilateral is `360^@`
`=>/_A+/_B+/_C+/_D=360^@`
`=>/_A+/_D+/_A+/_D=360^@` `[/_A=/_C` and `/_B=/_D]`
`=>2/_A=2/_D=360^@`
`=>/_A+/_D=180^@` [Co-interior angle]
`=>AB` parallel `DC`
Similarly,
`/_A+/_B+/_C+/_D=360^@`
`=>/_A+/_B+/_A+/_B=360^@` `[/_A=/_C` and `/_B=/_D]`
`=>2/_A+2/_B=360^@`
`=>/_A+/_B=180^@` [since, This is sum of interior angles on the same side of transversal `AB`]
`:.AD` parallel `BC`
So, `AB` parallel `DC` and `AD` parallel `BC`
`=>ABCD` is a parallelogram.
Hence Proved.