Question

Please HELP Provide the missing reasons for the proof. Given: ∠C ≅∠E Prove: ABC ~ DBE

Answer 1

The correct answers are:

#1) Given;
#2) Vertical angles are congruent; and 
#3) AA similarity theorem.

Explanation:

#1)  This is a "given" for the proof.  It requires no further explanation.
#2) ∠ABC and ∠DBE are opposite angles that share only a vertex.  This is the definition of vertical angles, and we know that vertical angles are congruent.
#3) The AA similarity theorem states that if two corresponding angles of two triangles are congruent, then the triangles are similar.  This is because all triangles have a sum of 180°.  If two of the angles are congruent, the third angle in both would have to be the same to make them equal 180°.  Thus the triangles are similar.

Answer 2

Reason:
1. Given
2. Angles opposite by the vertex
3. Two pair of corresponding angles are congruent (∠C ≅∠E and ∠ABC≅∠DBE)