Given: M is the midpoint of Prove: ΔPKB is isosceles

Triangle P B K is cut by perpendicular bisector B M. Point M is the midpoint of side P K.

It is given that M is the midpoint of and . Midpoints divide a segment into two congruent segments, so . Since and perpendicular lines intersect at right angles, and are right angles. Right angles are congruent, so . The triangles share , and the reflexive property justifies that . Therefore, by the SAS congruence theorem. Thus, because . Finally, ΔPKB is isosceles because it has two congruent sides.

corresponding parts of congruent triangles are congruent
base angles of isosceles triangles are congruent
of the definition of congruent segments
of the definition of a right triangle