To evaluate the given statements about quadrilateral ABCD, where AD is equal and parallel to BC, let's analyze each statement based on the properties of the quadrilateral:
A. β π΄π΅πΆβ β πΆπ·π΄
- This statement is true. Since AD is parallel to BC and they are cut by transversal AC, the alternate interior angles (β ABC and β CDA) are congruent.
B. π΅π·β―β―β―β―β―β―β―β―β―β₯π΄πΆβ―β―β―β―β―β―β―β―
- This statement cannot be assumed true without additional information. The fact that AD is parallel to BC does not imply that BD is perpendicular to AC.
C. π΅πΈβ―β―β―β―β―β―β―β―β πΈπ·β―β―β―β―β―β―β―β―β―
- This statement is true. Since diagonals of a quadrilateral with two pairs of opposite sides equal (and opposite sides parallel in this case) bisect each other at E, therefore BE is congruent to ED.
D. πβ π΄π΅πΆ+πβ π΅πΆπ·=180β
- This statement is true. Since AD is parallel to BC, the angles β ABC and β BCD are same-side interior angles, which means their sum equals 180Β°.
E. π΄π΅β―β―β―β―β―β―β―β―β πΆπ·β―β―β―β―β―β―β―β―β―
- This statement is true. Since AD is parallel to BC and they are equal in length, by the properties of parallel lines and equal lengths in quadrilaterals, AB and CD are also equal in length.
Based on the evaluations, the true statements about quadrilateral ABCD are:
- A. β π΄π΅πΆβ β πΆπ·π΄
- C. π΅πΈβ―β―β―β―β―β―β―β―β πΈπ·β―β―β―β―β―β―β―β―β―
- D. πβ π΄π΅πΆ+πβ π΅πΆπ·=180β
- E. π΄π΅β―β―β―β―β―β―β―β―β πΆπ·β―β―β―β―β―β―β―β―β―
Thus, the correct answers are: A, C, D, E.