10. (i) WE KNOW THAT A PARALLELOGRAM IS SUCH A QUADRILATERAL WHOSE OPPOSITE SIDES AND ANGLES ARE EQUAL AND ALSO THE OPPOSITE LINES ARE PARALLEL TOO...

Given" AC bisects angle A i.e it divides the angle two two equal parts angle 1 and angle 2 respectively.

To prove: AC bisects angle C

Proof: Assume that The diagonal even divides the angle C into Angle 3 and angle 4 respectively.

so, from this we can infer that angle 1=angle 3 and angle 2=angle 4 {alternate interior angles}

If the alternate the interior angles are equal then the angles are also equal.

therefore, AC also bisects angle C