Question

Given Segment BE = BC, which of the following angles are congruent?

a) ∠E = ∠C
b) ∠BEC = ∠BCE
c) ∠CEA = ∠BCE
d) ∠ABE = ∠BEA

Answer 1

The congruent angles given that Segment BE is equal to Segment BC are ∠BEC and ∠BCE because of the Isosceles Triangle Theorem, which states that the angles opposite to the congruent sides are congruent.

Step-by-step explanation:

To determine congruent angles given that Segment BE is equal to Segment BC, we must apply the properties of triangles. Specifically, if two sides of a triangle are congruent, the angles opposite those sides are also congruent because of the Isosceles Triangle Theorem. Therefore, the correct answer is (b) ∠BEC = ∠BCE.

Looking at the other options:

(a) ∠E and ∠C are not necessarily congruent because they are not opposite of the congruent segments.

(c) ∠CEA and ∠BCE don't have a congruence relation given in this context.

(d) ∠ABE and ∠BEA are not mentioned to have any congruent sides opposite to them.