Question

complete the two - column proof. given: x||y prove: ∠3≅∠5. m∠4 + m∠8 = 180°. m∠3 + m∠5 = m∠8 + m∠7. 1) m∠3 + m∠8 = m∠5 + m∠8 given. 2) m∠3 + m∠5 = m∠8 same - side interior angle postulate. 3) linear pair theorem. 4) transitive property of equality.

Explanation:

Step1: Start with given equation

Given \(m\angle3 + m\angle8=m\angle5 + m\angle8\).

Step2: Subtract \(m\angle8\) from both sides

By the subtraction - property of equality, \((m\angle3 + m\angle8)-m\angle8=(m\angle5 + m\angle8)-m\angle8\).

Step3: Simplify both sides

\(m\angle3=m\angle5\).

Step4: Recall angle - congruence definition

If two angles have equal measures, they are congruent. So \(\angle3\cong\angle5\).

Answer:

\(\angle3\cong\angle5\)