Question

question 17 of 39
what is the missing justification in the proof of the angle bisector
construction?
bm is congruent to bn.
mp is congruent to np.
bp is congruent to bp.
∠bmp is congruent to ∠bnp.
∠mbp is congruent to ∠nbp.
bp bisects ∠abc.
the segments were drawn by
the same compass setting.
the segments were drawn by
the same compass setting.
reflexive property
sss congruence
∠mbp and ∠nbp are congruent
and adjacent.

Explanation:

Step1: Analyze the proof structure

We have two triangles \(\triangle BMP\) and \(\triangle BNP\) that are congruent by SSS (Side - Side - Side) Congruence (\(\overline{BM}\cong\overline{BN}\), \(\overline{MP}\cong\overline{NP}\), \(\overline{BP}\cong\overline{BP}\)).

Step2: Relate the congruent triangles to the angles

When two triangles are congruent, their corresponding parts (including angles) are congruent. Since \(\angle MBP\) and \(\angle NBP\) are corresponding angles of congruent triangles \(\triangle BMP\) and \(\triangle BNP\), the justification for \(\angle MBP\cong\angle NBP\) is that corresponding parts of congruent triangles are congruent (CPCTC).

Answer:

Corresponding parts of congruent triangles are congruent (CPCTC)