Question

use the diagram shown. if ∠1 ≅ ∠3, which conclusion can be made? a. a ∥ b b. c ∥ d c. c ⊥ a d. b ⊥ d

Explanation:

Step1: Recall angle - pair relationships

$\angle1$ and $\angle3$ are vertical angles. Given $\angle1\cong\angle3$ is always true by the Vertical Angles Theorem. But we need to consider the relationship between the lines. $\angle1$ and $\angle3$ are also alternate interior angles for lines $c$ and $d$ with transversal $a$.

Step2: Apply the Alternate - Interior Angles Converse

If two lines are cut by a transversal and the alternate - interior angles are congruent, then the two lines are parallel. Since $\angle1$ and $\angle3$ are alternate interior angles for lines $c$ and $d$ and $\angle1\cong\angle3$, we can conclude that $c\parallel d$.

Answer:

B. $c\parallel d$