Question

for items 11 - 13, refer to the diagram. if $overline{ab}paralleloverline{cd}$, is $\triangle acdcong\triangle cab$? explain. a. yes; the triangles are congruent by angle - angle - side. b. yes; the triangles are congruent by angle - side - angle. c. yes; the triangles are congruent by side - angle - side. d. no; the triangles are not congruent.

Explanation:

Step1: Identify equal elements

Since $\overline{AB}\parallel\overline{CD}$, we have $\angle BAC=\angle ACD$ (alternate - interior angles). Also, $AC = AC$ (common side). But we don't have enough information about other equal angles or sides to prove congruence.

Step2: Check congruence criteria

The Angle - Angle - Side (AAS), Angle - Side - Angle (ASA), and Side - Angle - Side (SAS) criteria are not met.

Answer:

D. No; the triangles are not congruent