Question

∠sut and ∠wxz are supplementary. complete the proof that (overleftrightarrow{tv}paralleloverleftrightarrow{wy}).

Explanation:

Step1: Identify given info

Given: ∠SUT and ∠WXZ are supplementary.

Step2: Define supplementary angles

Supplementary angles sum to 180°, so \(m\angle SUT + m\angle WXZ = 180^\circ\).

Step3: Linear pair postulate

∠SUT and ∠TUX form a linear pair, so \(m\angle SUT + m\angle TUX = 180^\circ\).

Step4: Set sums equal

Both equal 180°, so \(m\angle SUT + m\angle WXZ = m\angle SUT + m\angle TUX\).

Step5: Subtract common angle

Subtract \(m\angle SUT\) from both sides: \(m\angle WXZ = m\angle TUX\).

Step6: Corresponding angles converse

∠WXZ and ∠TUX are corresponding angles; if equal, lines are parallel: \(TV \parallel WY\).

Answer:

The proof is completed with reasons: 1. Given; 2. Definition of supplementary angles; 3. Linear Pair Postulate; 4. Transitive Property of Equality; 5. Subtraction Property of Equality; 6. Converse of Corresponding Angles Theorem. Thus, \(TV \parallel WY\).