Question

Complete the paragraph proof.

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

Answer 1

Fill in the blank with: "PB = BK because corresponding parts of congruent triangles are congruent."

Full paragraph proof:

It is given that M is the midpoint of PK. Midpoints divide a segment into two congruent segments, so PM = MK. Since BM is perpendicular to PK, ∠PMB and ∠BMK are right angles. Right angles are congruent, so ∠PMB = ∠BMK. The triangles share BM, and the reflexive property gives BM = BM. Therefore ΔPMB ≅ ΔBMK by the SAS congruence theorem. Thus PB = BK because corresponding parts of congruent triangles are congruent. Finally, ΔPKB is isosceles because it has two congruent sides.