In the figure above, is the perpendicular bisector of . Three students explained how they proved .%0D%0A%0D%0ACory's explanation:%0D%0A%0D%0ASince is the perpendicular bisector of , and are right angles. That means that and are right triangles. Since point C is on the perpendicular bisector of , it is equidistant from point A and point B. That means that is congruent to . Also, is congruent to itself by the Reflexive Property of Congruence. So, by the Hypotenuse-Leg Theorem.%0D%0A%0D%0AJohn's explanation:%0D%0A%0D%0A is the perpendicular bisector of , so point C is equidistant from point A and point B. That means that is congruent to . A perpendicular bisector intersects a segment at its midpoint, so point D is the midpoint of . A midpoint divides a segment into two congruent segments, so is congruent to . Also, is congruent to itself by the Reflexive Property of Congruence. So, by the SSS Postulate.%0D%0A%0D%0AAlexis' explanation:%0D%0A%0D%0ASince is the perpendicular bisector of , and are right angles, and are therefore congruent to each other. A perpendicular bisector intersects a segment at its midpoint, so point D is the midpoint of . A midpoint divides a segment into two congruent segments, so is congruent to . Also, is congruent to itself by the Reflexive Property of Congruence. So, by the SAS Postulate.%0D%0A%0D%0AWhich explanation is incorrect?
