Question

given ed ≅ db, which statements about the figure are true? choose four correct answers. fa = 1/2fc. fc bisects db. eb is bisected by df. eb is a segment bisector.

Explanation:

Step1: Analyze segment - bisector concept

Since \(ED\cong DB\), point \(D\) is the mid - point of \(EB\). So \(EB\) is a segment bisected at \(D\). Also, if we assume \(FA = \frac{1}{2}FC\), it implies \(A\) is the mid - point of \(FC\) (if \(F\), \(A\), \(C\) are collinear). And \(EB\) is a segment bisector as \(D\) divides \(EB\) into two equal parts.

Step2: Check each statement

We can see that \(FA=\frac{1}{2}FC\), \(EB\) is bisected by \(D\) (so \(EB\) is a segment bisector) are valid based on the given \(ED\cong DB\).

Answer:

FA = 1/2FC, EB is a segment bisector