Questions: The two-column proof below describes the statements and reasons for proving that corresponding angles are co Step Statements Reasons --------- 1 UV WZ Given 2 Points S, Q, R, and T all lie on the same line. 3 m angle SQT=180° Given 4 m angle SQV+m angle VQT=m angle SQT Definition of a Straight Angle 5 m angle SQV+m angle VQT=180° Angle Addition Postulate 6 m angle VQT+m angle ZRS=180° Substitution Property of Equality 7 m angle SQV+m angle VQT-m angle VQT=m angle VQT+m angle ZRS-m angle VQT m / S D V=m / ZRS Same-Side Interior Angles Theorem 8 Substitution Property of Equality

Transcript text: The two-column proof below describes the statements and reasons for proving that corresponding angles are co Step | Statements | Reasons ---|---|--- 1 | $\overline{\mathrm{UV}} \| \overline{\mathrm{WZ}}$ | Given 2 | Points $\mathrm{S}, \mathrm{Q}, \mathrm{R}$, and T all lie on the same line. | 3 | $m \angle \mathrm{SQT}=180^{\circ}$ | Given 4 | $m \angle \mathrm{SQV}+m \angle \mathrm{VQT}=m \angle \mathrm{SQT}$ | Definition of a Straight Angle 5 | $m \angle \mathrm{SQV}+m \angle \mathrm{VQT}=180^{\circ}$ | Angle Addition Postulate 6 | $m \angle \mathrm{VQT}+m \angle \mathrm{ZRS}=180^{\circ}$ | Substitution Property of Equality 7 | $m \angle \mathrm{SQV}+m \angle \mathrm{VQT}-m \angle \mathrm{VQT}=m \angle \mathrm{VQT}+m \angle \mathrm{ZRS}-m \angle \mathrm{VQT}$ $m / \mathrm{S} D \mathrm{~V}=m / \mathrm{ZRS}$ | Sume-Side Interior Angles Theorem 8 | | Substitution Property of Equality