Question

which of the following must be true because the triangles are congruent? given: △aed ≅ △cbd a. none of the statements above must be true. b. d is the midpoint of eb c. eb bisects ac at d d. both of the statements above must be true.

Explanation:

Step1: Recall congruent - triangle properties

If $\triangle AED\cong\triangle CBD$, corresponding parts are equal.

Step2: Analyze each option

For option B, when two triangles are congruent, the intersection - point of their common line segment may be the mid - point of that segment. In this case, since $\triangle AED\cong\triangle CBD$, $D$ is the mid - point of $\overline{EB}$ because of the congruence of the triangles and the way they are related. For option C, there is no information from the congruence $\triangle AED\cong\triangle CBD$ that implies $\overline{EB}$ bisects $\overline{AC}$ at $D$.

Answer:

B. D is the midpoint of $\overline{EB}$