complete the paragraph proof.
given: m is the midpoint of $ \overline{pk} $
$ \overline{pk} \perp \overline{mb} $
prove: $ \triangle pkb $ is isosceles
it is given that m is the midpoint of $ \overline{pk} $ and $ \overline{pk} \perp \overline{mb} $.
midpoints divide a segment into two congruent
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

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# Brief Explanations:
We know that $\triangle PMB\cong\triangle KMB$ by $SAS$ (Side - Angle - Side) congruence theorem ($\overline{PM}\cong\overline{KM}$, $\angle PMB\cong\angle KMB$, $\overline{MB}\cong\overline{MB}$). When two triangles are congruent, their corresponding parts are congruent. In the context of $\triangle PMB$ and $\triangle KMB$, $\overline{PB}$ and $\overline{KB}$ are corresponding parts.

# Answer:
corresponding parts of congruent triangles are congruent

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