Question

given ( cdparallel fg ). enter segments in the blanks provided that would result in a true equation.
answer attempt 1 out of 2
( \frac{cd}{fg}=\frac{square}{square} )

Explanation:

Step1: Use the property of similar triangles

Since \(CD\parallel FG\), \(\triangle CED\sim\triangle FEG\) (by AA similarity criterion as \(\angle CED=\angle FEG\) (vertically - opposite angles) and \(\angle DCE=\angle GFE\) (alternate - interior angles as \(CD\parallel FG\))).

Step2: Apply the ratio of corresponding sides of similar triangles

For similar triangles \(\triangle CED\) and \(\triangle FEG\), the ratio of corresponding sides is equal. That is, \(\frac{CD}{FG}=\frac{CE}{FE}\) (corresponding sides of similar triangles are in proportion).

Answer:

$\frac{CD}{FG}=\frac{CE}{FE}$