Question

What are the missing parts that correctly complete the proof?

Given: Point Q is on the perpendicular bisector of segment M N. Prove: Point Q is equidistant from the endpoints of segment M N. Art: A horizontal line segment M N with X as the midpoint is drawn. A vertical line X Q is drawn. Q is above the horizontal line. The angle Q X N is labeled as a right angle. The line segments M X and N X are labeled with a single tick mark. A dotted line is used to connect point Q with point M. Another dotted line is used to connect point Q with point N.

Drag the answers into the boxes to correctly complete the proof.
Statement Reason
1. Point Q is on the perpendicular bisector of MN¯¯¯¯¯¯¯. Given
2. Definition of bisector
3. ​ ∠QXM ​ and ∠QXN are right angles. Definition of perpendicular
4. ∠QXM≅∠QXN
5. Reflexive Property of Congruence
6. △QXM≅△QXN
7. Corresponding parts of congruent triangles are congruent.
8. Point Q is equidistant from the endpoints of MN¯¯¯¯¯¯¯. Definition of equidistant
Definition of bisectorGivenASA Congruence PostulateSAS Congruence PostulateQM¯¯¯¯¯¯≅QN¯¯¯¯¯¯MX¯¯¯¯¯¯≅NX¯¯¯¯¯¯QX¯¯¯¯¯¯≅QX¯¯¯¯¯¯All right angles are congruent.

Answer 1

Point Q is equidistant from the endpoints of segment M N by Definition of equidistant.

Explanation:

Statement Reason

1. Point Q is on the perpendicular bisector of MN Given

2.MX≅NX- X is mid point of MN

3. ​ ∠QXM ​ and ∠QXN are right angles. Perpendicular line

4. ∠QXM≅∠QXN Both right angles

5.QX≅QX Reflexive Property

6. △QXM≅△QXN SAS Congruence

7.QM≅QN CPCTE property

8.Point Q is equidistant from the endpoints of MN . Definition of equidistant

Answer 2

Point Q is equidistant from the endpoints of segment M N by Definition of equidistant.

Explanation:

1. Point Q is on the perpendicular bisector of MN¯¯¯¯¯¯¯. Given

2.MX¯¯¯¯¯¯≅NX------------------------ Definition of bisector

3. ​ ∠QXM ​ and ∠QXN are right angles. Definition of perpendicular

4. ∠QXM≅∠QXN----------------------All right angles are congruent.

5.QX¯¯¯¯¯¯≅QX ----------------------- Reflexive Property of Congruence

6. △QXM≅△QXN -----------------------Congruence PostulateSAS

7.QM¯¯¯¯¯¯≅QN-------------------------------Corresponding parts of congruent triangles are congruent.

8.Point Q is equidistant from the endpoints of MN¯¯¯¯¯¯¯. Definition of equidistant