Question

1. why is

∠dca ≅ ∠1 and ∠ecb ≅ ∠2?
alt. int. angles are congruent
alt ext. angles are congruent
corresponding angles are congruent
consecutive interior angles are supplementary

Explanation:

Step1: Recall the definition of alternate interior angles

Alternate interior angles are formed when a transversal crosses two parallel lines. They are non - adjacent and lie between the two parallel lines, on opposite sides of the transversal.

Step2: Analyze the given situation

In the problem, line \(DE\) is parallel to line \(AB\) (since we drew a line parallel to \(AB\) through \(C\)). For \(\angle DCA\) and \(\angle1\), line \(AC\) is the transversal. For \(\angle ECB\) and \(\angle2\), line \(BC\) is the transversal. \(\angle DCA\) and \(\angle1\) are non - adjacent, lie between \(DE\) and \(AB\), and on opposite sides of transversal \(AC\). Similarly, \(\angle ECB\) and \(\angle2\) are non - adjacent, lie between \(DE\) and \(AB\), and on opposite sides of transversal \(BC\).

Answer:

Alt. Int. Angles are congruent