Question

1. the two trapezoids are similar. which is a correct proportion for corresponding sides?

ba/fe = fg/bc
ba/fe = ad/fg
ba/fe = ad/gd
ba/fe = cd/gd

Explanation:

Step1: Recall similarity property

For similar polygons, ratios of corresponding sides are equal. In similar trapezoids \(ABCD\) and \(AEFG\), \(BA\) corresponds to \(FE\), \(AD\) corresponds to \(GD\).

Step2: Check each option

• Option 1: \(\frac{BA}{FE}=\frac{FG}{BC}\), \(FG\) and \(BC\) are not corresponding sides.
• Option 2: \(\frac{BA}{FE}=\frac{AD}{FG}\), \(AD\) and \(FG\) are not corresponding sides.
• Option 3: \(\frac{BA}{FE}=\frac{AD}{GD}\), this is correct as \(BA\) and \(FE\), \(AD\) and \(GD\) are corresponding sides.
• Option 4: \(\frac{BA}{FE}=\frac{CD}{GD}\), \(CD\) and \(GD\) are not corresponding sides.

Answer:

\(\frac{BA}{FE}=\frac{AD}{GD}\) (the third - option in the original multiple - choice list)