Question

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

Given: PQ¯¯¯¯¯≅PR¯¯¯¯¯

Prove: ∠Q≅∠R

Answer 1

The data observed from the triangle are given below.

Statement                         Reason

$\overline{P Q} \cong \overline{P R}$                          Given

Draw $\overline{P M}$ so that M is the midpoint of QR.     Two points determine a line

$\overline{Q M} \cong \overline{R M}$                          Definition of midpoint

$\overline{P M} \cong \overline{P M}$                         Reflexive property of congruence

$\triangle P Q M \cong \Delta P R M$                SSS congruence postulate

$\angle \mathrm{Q} \cong \angle \mathrm{R}$                        CPCTC

SSS means side-side-side

CPCTC means corresponding parts of the congruence triangle are congruent.

Hence the given triangle is SSS congruence postulate