Question

Below is a two-column proof incorrectly proving that the three angles of ΔPQR sum 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 a Straight Angle m∠RPQ + m∠PRQ + m∠PQR = 180° Additive Property of Equality Which statement will accurately correct the two-column proof?

Answer 1

Answer:

m∠ZRY = 180° by Definition of Supplementary Angles

Step-by-step explanation:

I had a similar question and that line was correct on mine.

Answer 2

Answer:

Proof with statement is below.

Step-by-step explanation:

To Prove:

m∠RPQ + m∠PRQ + m∠PQR = 180°

Proof:

Draw line ZY parallel to segment PQ ............{Construction}

1. m∠ZRP + m∠PRQ + m∠QRY = m∠ZRY  .....{Angle Addition Postulate}

2. ∠ZRP ≅ ∠RPQ   ........{Alternate angles equal as ZY || PQ}

3. ∠QRY ≅ ∠PQR  .........{Alternate angles equal as ZY || PQ}

4. m∠RPQ + m∠PRQ + m∠PQR = m∠ZRY  ....{The three angles of ΔPQR equal 180° according to Substitution }

5. m∠ZRY = 180°   ......{Definition of a Straight Angle}

6. m∠RPQ + m∠PRQ + m∠PQR = 180° ...{Additive Property of Equality}...............PROVED