Question

parallelogram abcd is shown below.
thalia is using triangle congruence to prove properties of parallelograms.
if she wants to prove that \\(\overline{db}\\) bisects \\(\overline{ac}\\) and \\(\overline{ac}\\) bisects \\(\overline{db}\\), which triangle cong
a triangles abe and cde are congruent to each other.
b triangles abe and bce are congruent to each other.

Explanation:

To prove that the diagonals bisect each other, we need to show that the segments of each diagonal are equal. For parallelogram \(ABCD\), \(AB \parallel CD\) and \(AB = CD\). \(\angle ABE = \angle CDE\) and \(\angle BAE = \angle DCE\) (alternate interior angles). By ASA congruence, \(\triangle ABE \cong \triangle CDE\), which gives \(AE = CE\) and \(BE = DE\), proving the diagonals bisect each other. The other pair of triangles does not relate to the diagonal segments.

Answer:

A. Triangles ABE and CDE are congruent to each other.