Question

line $ell$ is the perpendicular bisector of segment $overline{wy}$. $z$ is a point on $ell$. nicolas noticed that $\triangle wxz$ and $\triangle yxz$ are congruent based on the side - angle - side congruency postulate. what theorem can we prove using these congruent triangles? choose 1 answer: a vertical angles are congruent. b measures of interior angles of a triangle sum to 180°. c a point on the perpendicular bisector of a line segment is equidistant from the segments endpoints. d any line segment is congruent to itself because every point on the segment maps to itself.

Explanation:

Since $\triangle WXZ\cong\triangle YXZ$ by SAS (Side - Angle - Side), we have $WZ = YZ$ as corresponding parts of congruent triangles are congruent. Point $Z$ is on the perpendicular bisector of $\overline{WY}$. This shows that a point on the perpendicular bisector of a line segment is equidistant from the segment's endpoints.

Answer:

C. A point on the perpendicular bisector of a line segment is equidistant from the segment's endpoints.