Question

prove that angles opposite to two equal sides of a triangle are equal.

Answer 1

we can define angle as an amount of rotation with respect to reference ray.

so see figure,
let reference line is AB

now Ray AC and Ray BC have same reference line and also both have same amount of rotation with reference to line AB ( same angle thita ) , so the side AC will be equal to side BC as the reference is same and angle also.

so we can say AC = BC = x
and angle CAB = angle CBA = thita.

Answer 2

To prove:ang PQM=angPRM
Construction:Drawing PM prependicular to QR
proof
1)in tri. PQM and PRM 1)
i)PM=PM(s) i)Common side
ii)PQ=PR(s) ii)isocelos triangle
iii)QM=MR iii)perpendicular line in an isocelos teiangle bisects the base.

2)Thus, tri PQM is congruent to 2)By SSS rule
tri PRM
3)Ang pQM=ang PRM 3)allangles of congruent triangles are equal
thus proved...