Proving S-A-S Congruency

Conjecture: If a point is on the perpendicular bisector of a line segment, then that point must be the same distance from each endpoint of the segment.
  1. Sketch and label a diagram of this situation.
    • Make note of any segments or angles you know to be congruent.
    • Make note of any other information you know.
  2. Find (or add auxiliary lines to find) 2 triangles that appear congruent.
  3. Shade in the 2 triangles using different colors.

Do you have enough information to prove that the 2 triangles in your diagram are congruent? Explain your reasoning.