Question

Draw out a two column proof for each problem below. Complete all problems on one page and upload ONE photo of the entire assignment Make sure your file/image is clear (not blurry) and easy to read. Problem 1. Congruent Triangle Proof (10 Points) Given: NQ is the bisector of MNP and NMQ ~ ZNPQ| Prove: A MNQA PNQ 0 Problem 2. Proof Involving CPCTC (14 Points) Given: S is the midpoint of QR QR PS and RSP and QSP are right angles. Prove: PR PQ S 0​

Answer 1

Two or more triangles are congruent if on comparison, they have equal lengths of sides, and measure of angles.

Therefore, the required proofs for each question are shown below:

Problem 1:

Congruent triangles are triangles with equal lengths of corresponding sides and measures of internal angles.

Thus,

                     STATEMENT                          REASON

1. <NMQ ≅ <NPQ                            Any point on a perpendicular bisector      

                                                        makes equal measure of angle with the

                                                        two ends of the line segment.

2. NQ ⊥ MP                                     Definition of a line.

3. MQ ≅ PQ                                     Equal segments of a bisected line.

4. MN ≅ PN                                     Any point on a perpendicular bisector    

                                                        is at the same distance to the

                                                        two ends of the line segment.

5. <MNQ ≅ <PNQ                           Equal measure of the bisected angle.

Problem 2:

A line segment is the shortest distance between two points.

            STATEMENTS                    REASONS

1. m<PSR  ≅ m<PSQ                A perpendicular bisector is always at a right  

                                                  angle to the bisected line segment.

2. m<RPS ≅ m<QPS                 Equal measure of the bisected angle.

3. RS ≅ QS                                Property of a bisected line segment.

4. PR ≅ PQ                                Any point on a perpendicular bisector    

                                                  is at the same distance to the two ends of  

                                                 the line segment.

For more clarifications on the perpendicular bisector of a line segment, visit: brainly.com/question/12475568

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