Question

eg || vx and su || eg. complete the proof that ( mangle rts + mangle vwy = 180^{circ} ).

Explanation:

Step1: Corresponding angles

Since \( \overleftrightarrow{SU}\parallel\overleftrightarrow{EG}\), by the Corresponding Angles Theorem, \( \angle RTS\cong\angle EFR\).

Step2: Same - side interior angles

Since \( \overleftrightarrow{EG}\parallel\overleftrightarrow{VX}\), by the Same - Side Interior Angles Theorem, \( m\angle EFR + m\angle VWY=180^{\circ}\).

Step3: Substitution

Because \( \angle RTS\cong\angle EFR\) (so \( m\angle RTS = m\angle EFR\)), we can substitute \( m\angle EFR\) with \( m\angle RTS\) in the equation \( m\angle EFR + m\angle VWY = 180^{\circ}\), getting \( m\angle RTS + m\angle VWY=180^{\circ}\).

Answer:

1. Corresponding Angles Theorem; 4. Same - Side Interior Angles Theorem; 5. Substitution Property of Equality.