Question

Given that AD and BC bisect each other at E, which of the following justifies ΔABE ≅ ΔDCE? A. Definition of Segment Bisector B. SSS Postulate C. Definition of Congruent Triangles D. SAS Postulate

Answer 1

The answer would be A.

Answer 2

Answer:

A. Definition of Segment Bisector

Step-by-step explanation:

One have to understand that according to data given in the question, we only know that AD and BC are bisected at the intersection point E. Now two triangles are formed which are ΔABE and ΔCDE.

Now by definition of segment bisector, we know that

AE = DE

BE = CE

Now, what is to understand that this information is based on the clue which is given in the question that AD and BC bisects each other. All the remaining options like SAS postulate, SSS postulate and definition of congruent triangle are not useful here if we don't know that these two lines bisect each other. Because, the fact that  

AE = DE

BE = CE

is only derived by the information that AD and BC bisect each other. Now we can derive SSS and SAS postulate both because we know by the theorems of trigonometry that if two sides of two different triangles are equal in length,  then their third sides must be equal, or when two lines bisect or intersect each other, vertical angles are always equal. So the answer is A.