Question

In the figure given below, BAC - DEC.
D
N
B
Which of the following conditions is sufficient to prove
that ACB is congruent to AECD?
A. ACCD
B. ZABC ZCDE
C. Cisthe mid point of BD
D. (The two triangles are always congruent.)
4120

Answer 1

option C is the correct answer that is C is the mid point of BD. Then the triangles will be congruent through ASA congruency id C is mid point of BD.

So, given Angle BAC=Angle DEC

So according to figure Angle ACB=Angle ECD

As two angles are equal then the third angles will also be equal.( by angle sum property).

So Angle ABC=Angle EDC

so now if they give C is the mid point then of BD, then BC=DC

So, In Triangle ACB and Triangle ECD,

Angle ACB=Angle ECD

BC=DC

Angle ABC=Angle EDC.

So by ASA (Angle Sude Angle) congruency we can tell both triangles are congruent.

So option C is the correct answer.