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This entry was posted in Geometry, Grades 9-12 and tagged perpendicular bisector theorem, proof of perpendicular bisector theorem, reflection postulate by Math Proofs. PA is congruent to PB since reflections preserve distance (by Reflection Postulate). Theorem 5-4 If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram. Theorem 5-3 Diagonals of a parallelogram bisect each other. Theorem 5-2 Opposite angles of a parallelogram are congruent. This is also by definition of reflection. Theorem 5-1 Opposite sides of a parallelogram are congruent. The reflection image of point A over line l is B. The reflection image of point P over line l is P itself. P is on the perpendicular bisector l of segment AB. The Angle Bisector Theorem says that an angle bisector of a triangle will divide the opposite side into two segments that are proportional to the other. If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment

That is given segment AB, perpendicular bisector l, and point P on l, then PA is congruent to PB.

definition transversal parallel lines conditional statement. The theorem states that given a segment, its perpendicular bisector, and a point on the perpendicular bisector, the endpoints of that segment is equidistant to the point on the perpendicular bisector. The corresponding angles postulate states that when a transversal. In this post, we use the Reflection Postulate to prove the Perpendicular Bisector Theorem. The angle bisectors of a triangle divide the opposite side into two segments proportional to the lengths of the other sides.

In the last two posts, we have discussed the properties of reflection and formalized our learning by enumerating the Reflection Postulate.