Select all statements that are true about the triangles. Triangles A B C ABC and D C B DCB are congruent by the Angle-Angle Triangle Congruence Theorem. Triangles A B C ABC and B C D BCD are congruent by the Angle-Side-Angle Triangle Congruence Theorem. Triangles A B C ABC and B C D BCD are congruent by the Side-Side-Side Triangle Congruence Theorem. Triangles A B C ABC and D C B DCB are congruent by the Side-Angle-Side Triangle Congruence Theorem. Triangles A B C ABC and D C B DCB are congruent by the Side-Side-Side Triangle Congruence Theorem. There is not enough information to determine if the triangles are congruent.

As we can seen from the given figure that two triangles are given.

The triangles ABC and BDC are :

Hence the option D and E are correct. i.e. congruent by the Side-Angle-Side Triangle Congruence Theorem.  

Learn more about the statements that are true about the triangles.

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The answer is below

Explanation:

Two triangles are said to be equal if all their three sides and all their three angles are exactly equal to each other.

Given triangle ABC and Triangle DCB, we can see that:

∠A = ∠D, |AB| = |CD|, |AC| = |BD| and they share the same side BC. Hence:

a) By the side-side-side (SSS) triangle congruence theorem the two triangles are equal. i.e. |AB| = |CD|, |AC| = |BD| and they share the same side BC.

b) By the side-angle-side (SAS) triangle congruence theorem the two triangles are equal. i.e. |AB| = |CD|, |AC| = |BD| and ∠A = ∠D.

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