A link to additional Clarifying Comments on this Assignment
1.3 - The Fundamental Property of a Perpendicular Bisector
(a) Write the definition of the perpendicular bisector of a segment.
(b) If AB is a segment and P is any point on the perpendicular bisector of AB, prove that the triangle PAB is isosceles (with PA = PB).
(c) If a triangle PAB is isosceles (with PA = PB), prove that P is a point on the perpendicular bisector of AB.
1.4 - Kite proofs using what you have recently proved.
Given the kite ABCD in problem 1.1, use 1.3 and the properties of isosceles triangles to give very short (one or two line) proofs of these statements:
(a) line AC is the perpendicular bisector of segment BD.
(b) ray AC bisects angle BAD and ray CA bisects angle DCB.
(c) triangle ABC is congruent to triangle ADC.