Question

ABC is a triangle in which BD bisects ABC and intersects AC at D, DE // CB. DE bisects AB at E. Prove that BE=ED.

a) BE=ED is not provable from the given information.
b) BE=ED is provable.
c) BE≠ED is provable.
d) None of the above.

Answer 1

To prove that BE=ED, we need to show that triangles BED and BEC are congruent. By using the Angle-Angle-Side congruence criterion, we can conclude that triangles BED and BEC are congruent. And if two triangles are congruent, then their corresponding sides are equal. Therefore, BE=ED.

Step-by-step explanation:

To prove that BE=ED, we need to show that triangles BED and BEC are congruent. From the given information, we know that BD bisects angle ABC, DE is parallel to CB, and DE bisects AB at E. Since BD bisects angle ABC, we have angle ABD = angle CBD. Since DE is parallel to CB, we have angle CED = angle ABC. And since DE bisects AB at E, we have angle BED = angle BEC. Therefore, by the Angle-Angle-Side congruence criterion, we can conclude that triangles BED and BEC are congruent. And if two triangles are congruent, then their corresponding sides are equal. Therefore, BE=ED.