Complete the paragraph proof.
given: m is the midpoint of pk
pk ⊥ mb
prove: △pkb is isosceles
it is given that m is the midpoint of pk and pk ⊥ mb. midpoints divide a segment into two congruent segments, so pm ≅ km. since pk ⊥ mb and perpendicular lines intersect at right angles, ∠pmb and ∠kmb are right angles. right angles are congruent, so ∠pmb ≅ ∠kmb. the triangles share mb, and the reflexive property justifies that mb ≅ mb. therefore, △pmb ≅ △kmb by the sas congruence theorem. thus, bp ≅ bk because
(corresponding parts of congruent triangles are congruent)
(base angles of isosceles triangles are congruent)
(of the definition of congruent segments)
(of the definition of isosceles triangles)
finally, △pkb is isosceles because it has two congruent sides.