Drag and drop a statement or reason to each box to complete the proof.

Given: PQ¯¯¯¯¯≅PR¯¯¯¯¯

Prove: ∠Q≅∠R


        Statement                                                                             Reason

PQ¯¯¯¯¯ ≅ PR¯¯¯¯¯                                                                   Given

Draw PM¯¯¯¯¯¯ so that M is the midpoint of QR¯¯¯¯¯ .             Two points determine a line.

 (                                    )                                                                Definition of midpoint

PM¯¯¯¯¯¯ ≅ PM¯¯¯¯¯¯                                                                (                                )

(                                    )                                                                 (                                 )

   ∠Q ≅ ∠R                                                                                      (                                  )


OPTIONS: CPCTC, QM¯¯¯¯¯≅ RM¯¯¯¯¯¯, △PQM ≅△ PRM , Reflexive Property of Congruence, SSS Congruence Postulate, HL Congruence Theorem 

AngelRay  Nov 14, 2017

This might help you!

\(\overline{QM}\cong\overline{RM}\) Definition of midpoint
\(\overline{PM}\cong\overline{PM}\) Reflexive Property of Congruence
\(\triangle PQM\cong\triangle PRM\) Side-Side-Side Triangle Congruence Postulate
TheXSquaredFactor  Nov 14, 2017


PQR is an isosceles triangle, and Q and P are reflected over the one line of symmetry, which happens to be PM if M is the midpoint of PR.

helperid1839321  Nov 14, 2017

Yes, you are right that the isosceles triangle theorem would end this problem in one step.

TheXSquaredFactor  Nov 17, 2017

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