What’s the statement and reasons for this

Question

given: S is the midp of PR

           QS is the altitude from Q to PR

 

Prove: triangle PQS is congrurent to triangle RSQ

Answer 1

Your proof statement needs to be ΔPQS to ΔRQS; otherwise, corresponding parts don't match up.

 

Statements                                                 Reasons                     

1. S is the midpoint of PR                          1.  Given

2. PS ≅ SR                                                  2. Definition of a midpoint

3. QS is the altitude to PR                         3. Given

4. QS ⊥ PR                                                  4. Definition of an altitude

5. ∠PSQ and ∠ RSQ are right angles         5. Definition of perpendicular

6. ∠PSQ ≅ ∠RSQ                                         6.  Right angles are congruent

7. QS ≅ QS                                                 7. Reflexive Property

8. ∴ ΔPQS ≅ ΔRQS                                     8. SAS

 

All of the segments should have bars over them. I couldn't do that on the computer.

Answer 2

 

S is the midpoint of PR            given

 

PS = RS                                 definition of midpoint

 

QS = SQ                               reflexive

 

QS is the altitude                 given

 

QS is perpendicular             definition of altitude

 to PR

 

Angle QSP and QSR              definition of perpendicular; transitive

are both equal right angles

 

Triangles PQS and RQS        LL: leg leg theorem for   

are congruent                     right triangles; You can also

                                         use SAS