It is given that M is the midpoint of line segment PK and line segment PK perpendicular to line segment MB Midpoints divide a segment into two congruent segments, so line segment PM is congruent to line segment KM Since line segment PK perpendicular to line segment MB and perpendicular lines intersect at right angles, angle PMB and angle KMB are right angles. Right angles are congruent, so angle PMB is congruent to angle KMB The triangles share line segment MB , and the reflexive property justifies that line segment MB is congruent to line segment MB Therefore, triangle PMB is congruent to triangle KMB by the SAS congruence theorem. Thus, line segment BP is congruent to line segment BK because _____________. Finally, triangle PKB is isosceles because it has two congruent sides.
Answer
A
of the definition of congruent segments
B
corresponding parts of congruent triangles are congruent
C
base angles of isosceles triangles are congruent
D
of the definition of a right triangle
Explanation
Since triangle PMB is congruent to triangle KMB, their corresponding sides are congruent. In this correspondence, side BP matches side BK, so BP ≅ BK by the rule that corresponding parts of congruent triangles are congruent. Therefore, triangle PKB has two congruent sides and is isosceles.
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