Question

Select the correct answer from each drop-down menu. Given: mn is the perpendicular bisector of ab. Prove: am=bm. A diagram of the triangle amb. n is the midpoint of the base ab. A double-sided arrow line connects mn. Complete the proof.

1) Definition of a perpendicular bisector
2) Definition of a midpoint
3) All right angles are congruent
4) Reflexive property of congruence
5) SAS CPCTC

Answer 1

The perpendicular bisector mn of ab implies that AM and BM are congruent because of the definition of a midpoint, congruence of right angles, and the SAS Postulate leading to CPCTC.

Step-by-step explanation:

Proving AM = BM in Triangle AMB

Given that line segment mn is the perpendicular bisector of line segment ab, we need to prove that AM equals BM.

If mn bisects ab at its midpoint, segment AM is congruent to segment BM, since the definition of a midpoint (Definition of a midpoint) implies that the segments on either side are equal.

Furthermore, because mn is perpendicular to ab, angles AMN and BMN are right angles, which are congruent based on the principle that All right angles are congruent.

Thus, we have two pairs of congruent sides and a pair of congruent angles between them, which allows us to use the SAS Postulate to establish that triangles AMN and BMN are congruent. Consequently, by CPCTC (Corresponding Parts of Congruent Triangles are Congruent), we can conclude that side AM is congruent to side BM.