Question

select the correct answer from each drop - down menu. in the figure, a || b, and both lines are intersected by transversal t. complete the statements to prove that m∠1 = m∠5. a || b (given) m∠1 + m∠3 = 180° (linear pair theorem) m∠5 + m∠6 = 180° (linear pair theorem) m∠1 + m∠3 = ∠5 + ∠6 ( ) m∠3 = m∠6 ( ) m∠1 = m∠5 (subtraction property of equality)

Explanation:

Step1: Substitute equal - angle sums

Since \(m\angle1 + m\angle3=180^{\circ}\) and \(m\angle5 + m\angle6 = 180^{\circ}\), by the Transitive Property of Equality, \(m\angle1 + m\angle3=m\angle5 + m\angle6\).

Step2: Use corresponding - angle property

Because \(a\parallel b\), \(\angle3\) and \(\angle6\) are corresponding angles, so \(m\angle3 = m\angle6\) (Corresponding Angles Postulate).

Answer:

First blank: Transitive Property of Equality
Second blank: Corresponding Angles Postulate