Question

segments ab and fb are congruent. segments ac and fd are congruent. segments bc and bd are congruent. overlapping triangles which of the following relationships proves why △abc and △fbd are congruent? sss hl saa sas

Explanation:

Step1: Identify the congruent sides

From the given information:

• \(AB = FB\) (Segments \(AB\) and \(FB\) are congruent)
• \(AC = FD\) (Segments \(AC\) and \(FD\) are congruent)
• \(BC = BD\) (Segments \(BC\) and \(BD\) are congruent)

Step2: Recall the SSS congruence criterion

The SSS (Side - Side - Side) congruence criterion states that if three sides of one triangle are equal to the three corresponding sides of another triangle, then the two triangles are congruent.

Since in \(\triangle ABC\) and \(\triangle FBD\), \(AB = FB\), \(AC = FD\), and \(BC = BD\), we can use the SSS criterion.

Answer:

SSS