Question

Plz help. Draw line ZY parallel to segment PQ Construction

m∠ZRP + m∠PRQ + m∠QRY = m∠ZRY Angle Addition Postulate

∠ZRP ≅ ∠RPQ Alternate Interior Angles Theorem

∠QRY ≅ ∠PQR Alternate Interior Angles Theorem

m∠RPQ + m∠PRQ + m∠PQR = m∠ZRY Substitution

m∠ZRY = 180° Definition of a Straight Angle

m∠RPQ + m∠PRQ + m∠PQR = 180° Additive Property of Equality



Which statement will accurately correct the two-column proof?

A. The measure of angle ZRY equals 180° by definition of supplementary angles.

B. Angles QRY and PQR should be proven congruent before the construction of line ZY.

C. The three angles of ΔPQR equal 180° according to Substitution.

D. Line ZY should be drawn parallel to segment QR.

Answer 1

Angles QRY and PQR should be proven congruent after the construction of line ZY.

Explanation:

Answer 2

A statement that will accurately correct the two-column proof is: C. The three angles of ΔPQR equal 180° according to Substitution.

In Mathematics and Geometry, a supplementary angle refers to two (2) angles or arc whose sum is equal to 180 degrees.

Additionally, the sum of all of the angles on a straight line is always equal to 180 degrees. Since line ZY parallel to segment PQ, we have the following angle sum based on Angle Addition Postulate;

m∠ZRP + m∠PRQ + m∠QRY = m∠ZRY

By using the substitution method, we can reasonably infer and logically deduce the following supplementary angles in triangle PQR:

m∠RPQ + m∠PRQ + m∠PQR = m∠ZRY

m∠RPQ + m∠PRQ + m∠PQR = 180°

Complete Question:

Below is a two-column proof incorrectly proving that the three angles of ΔPQR sum to 180°:

Which statement will accurately correct the two-column proof?

A. The measure of angle ZRY equals 180° by definition of supplementary angles.

B. Angles QRY and PQR should be proven congruent before the construction of line ZY.

C. The three angles of ΔPQR equal 180° according to Substitution.

D. Line ZY should be drawn parallel to segment QR.