Question

Line segments AD and BE intersect at C, and triangles ABC and DEC are formed. They have the following characteristics:

∠ACB and ∠DCE are vertical angles
∠B = ∠E
∠BC = ∠EC

Which congruence theorem can be used to prove triangle ∠ABC congruent to triangle ∠DEC?
a. HL
b. ASA
c. SSS
d. SAS

Answer 1

The congruence theorem that can be used to prove triangle ABC congruent to triangle DEC is SAS (Side-Angle-Side).

Step-by-step explanation:

The congruence theorem that can be used to prove triangle ABC congruent to triangle DEC is SAS (Side-Angle-Side). This theorem states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

In this case, we have triangle ABC and triangle DEC, where the following statements are given:

1. 
   
3. ∠ACB and ∠DCE are vertical angles
4. 
   
6. ∠B = ∠E
7. 
   
9. ∠BC = ∠EC

Using the SAS congruence theorem, we can conclude that triangle ABC is congruent to triangle DEC.