Question

1. using the diagram below, find all angles congruent to the given angle given ab||cd.

∠b≅∠__,∠,∠ ∠a≅∠,∠,∠__

Explanation:

Step1: Recall parallel - line angle relationships

When two parallel lines \(AB\parallel CD\) are cut by a transversal, vertical angles are congruent and corresponding angles are congruent.

Step2: Identify congruent angles for \(\angle b\)

\(\angle b\) and \(\angle c\) are vertical angles, so \(\angle b\cong\angle c\). \(\angle b\) and \(\angle f\) are corresponding angles, so \(\angle b\cong\angle f\). \(\angle f\) and \(\angle h\) are vertical angles, so \(\angle b\cong\angle h\).

Step3: Identify congruent angles for \(\angle a\)

\(\angle a\) and \(\angle d\) are vertical angles, so \(\angle a\cong\angle d\). \(\angle a\) and \(\angle e\) are corresponding angles, so \(\angle a\cong\angle e\). \(\angle e\) and \(\angle g\) are vertical angles, so \(\angle a\cong\angle g\).

Answer:

\(\angle b\cong\angle c,\angle f,\angle h\); \(\angle a\cong\angle d,\angle e,\angle g\)