Question

question 6 of 10
determine which postulate or theorem can be used to prove that
$\triangle abc\cong\triangle edc$.
a. sas
b. aas
c. sss
d. asa

Explanation:

Step1: Identify vertical angles

Vertical angles are equal. So, \(\angle ACB=\angle ECD\)

Step2: Analyze given information

We are given that \(\angle B=\angle D\) (marked in the figure) and \(BC = DC\) (marked in the figure).

Step3: Apply AAS theorem

The AAS (Angle - Angle - Side) theorem states that if two angles and a non - included side of one triangle are congruent to two angles and the corresponding non - included side of another triangle, then the two triangles are congruent. Here, \(\angle B=\angle D\), \(\angle ACB=\angle ECD\) (vertical angles), and \(BC = DC\) (non - included side).

Answer:

B. AAS