Question

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


Statements Reasons
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 Supplementary Angles
m∠RPQ + m∠PRQ + m∠PQR = 180° Substitution


Which statement will accurately correct the two-column proof?
The measure of angle ZRY equals 180° by definition of a straight angle.
Angles QRY and PQR should be proven congruent before 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.

Answer 1

maybe more usefully than you post / try draw this triangle / angles cases

@Laylalyssa