Question

segments, so ( overline{pm} cong overline{km} ) since ( overline{pk} perp overline{mb} ) and perpendicular lines intersect at right angles, ( angle pmb ) and ( angle kmb ) are right angles right angles are congruent, so ( angle pmb cong angle kmb ) the triangles share ( overline{mb} ) and the reflexive property justifies that ( overline{mb} cong overline{mb} ) therefore, ( \triangle pmb cong \triangle kmb ) by the sas congruence theorem thus, ( overline{bp} cong overline{bk} ) because ____________ finally, ( \triangle pkb ) 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

Explanation:

We know that if two triangles are congruent, then their corresponding parts (sides and angles) are congruent. Here, since \(\triangle PMB\cong\triangle KMB\) (by SAS congruence theorem), when we consider the sides \(BP\) and \(BK\), they are corresponding sides of the congruent triangles \(\triangle PMB\) and \(\triangle KMB\).

Answer:

corresponding parts of congruent triangles are congruent