High School

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Select all statements that are true about the triangles.

A. Triangles \(ABC\) and \(DCB\) are congruent by the Angle-Angle Triangle Congruence Theorem.
B. Triangles \(ABC\) and \(BCD\) are congruent by the Angle-Side-Angle Triangle Congruence Theorem.
C. Triangles \(ABC\) and \(BCD\) are congruent by the Side-Side-Side Triangle Congruence Theorem.
D. Triangles \(ABC\) and \(DCB\) are congruent by the Side-Angle-Side Triangle Congruence Theorem.
E. Triangles \(ABC\) and \(DCB\) are congruent by the Side-Side-Side Triangle Congruence Theorem.
F. There is not enough information to determine if the triangles are congruent.

Answer :

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

The triangles ABC and BDC are :

  • AB = CD
  • AC = BD
  • BC = BC
  • Hence using the SSS theorem of the triangle, the triangle ABC and DBC are congruent, Thus the angle A is equal to angle D.

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.

brainly.com/question/25258416.

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Rewritten by : Jeany

Final answer:

The triangles cannot be determined to be congruent

Explanation:

The correct statement is that there is not enough information to determine if the triangles are congruent.

The Angle-Angle Triangle Congruence Theorem states that if two angles in one triangle are congruent to two angles in another triangle, then the triangles are congruent. However, in the given options, Triangle ABC and Triangle DCB are declared congruent by the Angle-Angle Triangle Congruence Theorem, which is incorrect because the sides are not mentioned to be congruent.

Therefore, the answer is that there is not enough information to determine if the triangles are congruent.

Learn more about Triangle Congruence here:

https://brainly.com/question/20521780

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