Question

course challenge
google classroom 1 microsoft teams 1
consider this diagram of quadrilateral abcd, which is not drawn to scale.
diagram of quadrilateral abcd with diagonals intersecting at e, and markings indicating congruent segments
which two statements must be true based on the information indicated by the diagram?
choose 2 answers:

• $\angle cde \cong \angle ecd$
• $\angle abe \cong \angle cde$
• $\overline{ac} \cong \overline{bd}$
• $\overline{ae} \cong \overline{ce}$

Explanation:

1. Analyze \( AE \cong CE \): The diagram shows the diagonals of quadrilateral \( ABCD \) intersecting at \( E \), with markings indicating \( AE = CE \) (since the segments from \( E \) on diagonal \( AC \) are marked equal). So \( AE \cong CE \) must be true.
2. Analyze \( \angle ABE \cong \angle CDE \): If \( ABCD \) is a parallelogram (implied by diagonals bisecting each other, from \( AE \cong CE \) and likely \( BE \cong DE \) from markings), then \( AB \parallel CD \) and \( AB = CD \). By alternate interior angles or triangle congruence (e.g., \( \triangle ABE \cong \triangle CDE \) by SAS if diagonals bisect each other), \( \angle ABE \cong \angle CDE \).
3. Eliminate other options: \( \angle CDE \cong \angle ECD \) would require \( CD = DE \), not indicated. \( AC \cong BD \) is true for rectangles/squares, but the diagram only shows diagonals bisecting each other (not necessarily equal), so not guaranteed.

Answer:

D. \( AE \cong CE \)
B. \( \angle ABE \cong \angle CDE \)