Question

copy the triangle and highlight congruent parts. mark and highlight additional congruent parts that can be proved congruent on your paper. explain why the parts are congruent. determine if the triangles are congruent and by what method. reflexive property, sss vertical ∠s ≅, sas vertical ∠s ≅, ssa, as not ≅ alternate interior ∠s ≅, sas

Explanation:

Step1: Identify Congruent Sides

From the figure, \(AB = CB\) and \(BE=BD\) (marked as equal).

Step2: Identify Congruent Angles

\(\angle ABE\) and \(\angle CBD\) are vertical angles. By the vertical - angles theorem, \(\angle ABE\cong\angle CBD\).

Step3: Apply Congruence Criterion

In \(\triangle ABE\) and \(\triangle CBD\), we have two sides and the included angle congruent. That is, \(AB = CB\), \(\angle ABE=\angle CBD\), and \(BE = BD\). By the Side - Angle - Side (SAS) congruence criterion.

Answer:

Vertical \(\angle s\cong\), \(SAS\) (the second option: Vertical \(\angle s\cong\), \(SAS\))