Question

in the figure below, for the triangle △abc and triangle △def, the sides ab = de, bc = ef and ac = df are corresponding sides of equal length. which statement best describes the relationship between these two triangles? they are neither similar nor congruent triangles. they are similar but not congruent triangles. they are not congruent triangles. they are congruent triangles.

Explanation:

Step1: Recall triangle - congruence criteria

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

Step2: Analyze given information

We are given that \(AB = DE\), \(BC=EF\), and \(AC = DF\), which satisfies the SSS congruence criterion for \(\triangle ABC\) and \(\triangle DEF\).

Answer:

They are congruent triangles.