Respuesta :

ASA because angle B and D are congruent, side BC and DC are congruent and angle C and angle C are congruent because they are vertical.

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Answer:

ASA

Step-by-step explanation:

According to the graph, givens are

[tex]BC \cong CD[/tex]

[tex]\angle ABC \cong \angle EDC[/tex]

Now, [tex]\angle ACB[/tex] and [tex]\angle ECD[/tex] are vertical angles, because they are in opposite sides of C, and they don't have any side in common. By congruence postulates, we know that [tex]\angle ACB \cong \angle ECD[/tex]

So, at this point, we have three elements congruent:

[tex]BC \cong CD[/tex]

[tex]\angle ABC \cong \angle EDC[/tex]

[tex]\angle ACB \cong \angle ECD[/tex]

This allow us to use ASA postulate, that is, Angle-Side-Angle postulate, because we have congruence between corresponding angles and the side in between.

In addition, the ASA postulate states that if two triangles have two corresponding angles congruent, and the sides between them are also congruent, then those triangles are congruent.

Therefore, the right answer is ASA.

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