Question

given: $overleftrightarrow{ab}$ is the perpendicular bisector of $overline{cd}$ prove: point a is equidistant from points c and d proof: statements reasons 1. $overleftrightarrow{cd}$ is the perpendicular bisector of $overline{ab}$ given 2. $overline{cm}congoverline{dm}$ a perpendicular bisector divides a segment into two congruent segments 3. $angle{cma}$ and $angle{dma}$ are right angles a perpendicular bisector forms right angles with the segment it bisects 4. $angle{cma}congangle{dma}$ right angles are congruent 5. $overline{am}congoverline{am}$ reflexive property 6. draw $overline{ca}$ two points determine a segment 7. draw $overline{da}$ two points determine a segment 8. $\triangle{acm}cong\triangle{adm}$ side - angle - side 9. $overline{ac}congoverline{ad}$ 10. point a is equidistant from points c and d the shortest distance between two points is the length of the segment joining them which of the following reasons completes the proof? a. perpendicular bisectors form congruent right angles b. perpendicular segments form angles of equal measure. c. corresponding parts of congruent triangles are congruent d. a bisector divides a segment into two congruent segments

Explanation:

We have proven that $\triangle ACM\cong\triangle ADM$ in step 8. To go from congruent triangles to congruent corresponding sides ($\overline{AC}\cong\overline{AD}$ in step 9), the reason is that corresponding parts of congruent triangles are congruent.

Answer:

C. Corresponding parts of congruent triangles are congruent