Question

given that $overline{ba}paralleloverline{ce}$, select which type of angle each pair below is and then tell whether the pair is congruent or supplementary.
(a) 7. $angle bae$ and $angle ced$
a. interior angles on the same side of the transversal; congruent
b. corresponding angles; congruent
c. alternate exterior angles; congruent
d. adjacent angles; congruent
e. alternate interior angles; congruent

1. $angle abc$ and $angle bce$

a. interior angles on the same side of the transversal; supplementary
b. adjacent angles; supplementary
c. alternate exterior angles; congruent
d. corresponding angles; congruent
e. alternate interior angles; congruent

1. $angle bce$ and $angle ecd$

a. adjacent angles (linear pair); supplementary
b. corresponding angles; supplementary
c. alternate exterior angles; congruent
d. interior angles on the same side of the transversal; supplementary
e. alternate interior angles; supplementary

Explanation:

Step1: Recall angle - pair relationships

When two parallel lines are cut by a transversal, different types of angle - pairs have specific properties.

Step2: Analyze \(\angle BAE\) and \(\angle CED\)

\(\overline{BA}\parallel\overline{CE}\) and \(AD\) is a transversal. \(\angle BAE\) and \(\angle CED\) are corresponding angles. Corresponding angles formed by two parallel lines and a transversal are congruent. So for \(\angle BAE\) and \(\angle CED\), they are corresponding angles; congruent.

Step3: Analyze \(\angle ABC\) and \(\angle BCE\)

\(\overline{BA}\parallel\overline{CE}\) and \(BC\) is a transversal. \(\angle ABC\) and \(\angle BCE\) are alternate interior angles. Alternate interior angles formed by two parallel lines and a transversal are congruent.

Step4: Analyze \(\angle BCE\) and \(\angle ECD\)

\(\angle BCE\) and \(\angle ECD\) share a common side \(CE\) and a common vertex \(C\), and they form a linear - pair (a straight - line \(BD\)). Adjacent angles that form a linear - pair are supplementary.

Answer:

1. B. Corresponding angles; congruent
2. E. Alternate interior angles; congruent
3. A. Adjacent angles (linear pair); supplementary