164k views
3 votes
Given Segment BE = BC, which of the following angles are congruent?

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

User Thufir
by
7.3k points

1 Answer

3 votes

Final answer:

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.

User ForeignerBR
by
8.8k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.