Question

given: $overline{ab}paralleloverline{dc}$, $angle acongangle d$. prove: $\triangle abccong\triangle dcb$. isabelle proves that the triangles are congruent by using the parallel lines to determine a second set of angles are congruent. what statement and reason could she have used? $angle abccongangle dcb$; alternate interior angles of parallel lines are congruent. $angle abccongangle bac$; corresponding angles of parallel lines are congruent. $angle cabcongangle dcb$; alternate interior angles of parallel lines are congruent. $angle acdcongangle abd$; corresponding angles of parallel lines are congruent.

Explanation:

Step1: Recall angle - congruence rules for parallel lines

When two parallel lines are given (here $\overline{AB}\parallel\overline{DC}$), we use the properties of angles formed by parallel lines and a transversal.

Step2: Analyze the position of angles

$\angle ABC$ and $\angle DCB$ are alternate - interior angles formed by the parallel lines $\overline{AB}$ and $\overline{DC}$ with the transversal $\overline{BC}$.

Answer:

$\angle ABC\cong\angle DCB$; alternate interior angles of parallel lines are congruent.