Question

statements reasons draw line zy parallel to $overline{pq}$ construction $mangle zrp + mangle prq + mangle qry = mangle zry$ angle addition postulate $angle zrpcongangle rpq$ alternate interior angles theorem $angle qrycongangle pqr$ alternate interior angles theorem $mangle rpq + mangle prq + mangle pqr = mangle zry$ substitution $mangle zry = 180^{circ}$ definition of a straight angle $mangle rpq + mangle prq + mangle pqr = 180^{circ}$ additive property of equality which statement will accurately correct the two - column proof? the measure of angle zry equals $180^{circ}$ by definition of supplementary angles. angles qry and pqr should be proven congruent before the construction of line zy. the three angles of $\triangle pqr$ equal $180^{circ}$ according to substitution. line zy should be drawn parallel to segment qr.

Explanation:

1. Analyze each option:

• The measure of $\angle ZRY$ equals $180^{\circ}$ by the definition of a straight - angle, not supplementary angles.
• Angles $\angle QRY$ and $\angle PQR$ are proven congruent after constructing line $ZY$ parallel to $\overline{PQ}$ using the alternate - interior angles theorem.
• The three angles of $\triangle PQR$ equal $180^{\circ}$ because $\angle ZRY = 180^{\circ}$ and through substitution of congruent alternate - interior angles. This is correct.
• Line $ZY$ is drawn parallel to $\overline{PQ}$ to use the alternate - interior angles theorem, not $\overline{QR}$.

Answer:

The three angles of $\triangle PQR$ equal $180^{\circ}$ according to Substitution.