Question

batman is trying a new design signal for his sidekick, robin. the following design is shown below.
db = ca
given △dab and △cba with sides and angles as marked, select the postulate or theorem that proves these triangles are congruent
○ angle angle side congruence theorem ○ side angle side congruence postulate
○ side side side congruence postulate ○ these triangles are not congruent.
○ angle side angle congruence postulate ○ hypotenuse leg congruence theorem

Explanation:

Step1: Identify common side

In \(\triangle DAB\) and \(\triangle CBA\), \(AB = BA\) (common side).

Step2: Analyze given side and angles

We are given \(DB = CA\). Also, \(\angle DAB=\angle CBA\) (if we assume the marked angles). So we have two angles and a non - included side.
By the Angle Angle Side (AAS) Congruence Theorem: 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.

Answer:

Angle Angle Side Congruence Theorem