Question

11 multiple choice 1 point the following triangles can be proven congruent by which theorem, if any? given: \\( \overline { b c } \cong \overline { d c }, \overline { a c } \cong \overline { e c } \\) sas sss asa aas hl cannot be proven congruent clear my selection

Explanation:

Step1: Identify the included angle

The vertical angles at point \(C\) are congruent. Let \(\angle ACB\) and \(\angle ECD\) be the vertical angles. By the vertical - angles theorem, \(\angle ACB\cong\angle ECD\).

Step2: Check the congruent sides and included angle

We are given that \(BC\cong DC\) and \(AC\cong EC\). In \(\triangle ABC\) and \(\triangle EDC\), we have two sides and the included angle.
For \(\triangle ABC\) and \(\triangle EDC\), \(BC = DC\), \(\angle ACB=\angle ECD\) (vertical angles), and \(AC = EC\).

Answer:

A. SAS