Question

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

Answer 1

Statements Reasons
∠QRY ≅ ∠PQR Alternate Interior Angles Theorem
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
m∠RPQ + m∠PRQ + m∠PQR = m∠ZRY Substitution
m∠ZRY = 180° Definition of a Straight Angle
m∠RPQ + m∠PRQ + m∠PQR = 180° Substitution

Answer 2

Which statement will accurately correct the two-column proof?
The measure of angle ZRY equals 180° by definition of supplementary angles.

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

The three angles of ΔPQR equal 180° according to the Transitive Property of Equality.

Line ZY should be drawn parallel to segment QR.