Question

1. in the diagram, the vertical lines are parallel. name all pairs of similar triangles.

Explanation:

Step1: Use the AA (Angle - Angle) similarity criterion

Since the vertical lines are parallel, corresponding angles are equal. For example, in \(\triangle AGC\) and \(\triangle AEB\), \(\angle A=\angle A\) (common angle) and \(\angle AGC=\angle AEB\) (corresponding angles as \(GC\parallel EB\)). Similarly, in \(\triangle AFC\) and \(\triangle AED\), \(\angle A=\angle A\) (common angle) and \(\angle AFC=\angle AED\) (corresponding angles as \(FC\parallel ED\)). Also, in \(\triangle AGB\) and \(\triangle AFC\), \(\angle A=\angle A\) (common angle) and \(\angle AGB=\angle AFC\) (corresponding angles as \(GB\parallel FC\)).

Step2: List the similar triangle pairs

By AA similarity:

• \(\triangle AGB\sim\triangle AFC\)
• \(\triangle AGB\sim\triangle AED\)
• \(\triangle AFC\sim\triangle AED\)

Answer:

\(\triangle AGB\sim\triangle AFC\), \(\triangle AGB\sim\triangle AED\), \(\triangle AFC\sim\triangle AED\)