Question

given: \\( \overline{ad} \parallel \overline{bc} \\) \\( \overline{ab} \\) bisects \\( \angle cad \\) prove: \\( \angle 1 \cong \angle 4 \\)

Explanation:

Step1: Use the property of angle bisector

Since \(AB\) bisects \(\angle CAD\), by the definition of angle bisector, \(\angle1=\angle3\)

Step2: Use the property of parallel lines

Because \(AD\parallel BC\), by the alternate - interior angles theorem, \(\angle3 = \angle4\)

Step3: Use the transitive property of congruence

Since \(\angle1=\angle3\) and \(\angle3=\angle4\), then \(\angle1=\angle4\) (transitive property: if \(a = b\) and \(b = c\), then \(a = c\))

Answer:

The proof is completed as above to show \(\angle1\cong\angle4\)