angle pqr and angle rqs are linear pair of angles that are congruent and pq=qs

Question

need a diagram and need proof for the diagram

Answer 1

Since the two angles are linear and congruent, then if x is the measure of either angle, their sum is 2x, and 2x=180, making x a right angle, because they lie on a straight line. The line segments are also equal, so we have a perpendicular bisector, and we get an isosceles triangle when the points are joined.