Question

Look at the figure shown below:

RQ is a segment on which a perpendicular bisector PS is drawn. S is the midpoint of RQ. Which step should be used to prove that point P is equidistant from points R and Q?

Answer 1

One possible answer is:

Draw segments from P to R and from P to Q; the triangles formed will be congruent by the SAS congruence theorem.

Step-by-step explanation:

Drawing segments from P to R and from P to Q creates triangles PSR and PSQ.

In these two triangles, we know that RS ≅ SQ and PS≅PS.

Since PS is the perpendicular bisector of RQ, we also know that ∠PSR = 90; this is the same as ∠PSQ, so the two angles are congruent.

This means we have two sides and the angle between them congruent; this is the SAS postulate, which proves the triangles are congruent.

Since the triangles are congruent, all corresponding sides are congruent; this means that PR ≅ PQ.