Triangles ABC and ADC are shown below. Paul claims that triangles ABC and ADC are congruent.

Based on the diagram, determine whether each statement below can be used to justify the claim. Select Yes or No for each statement.
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Triangles ABC and ADC are congruent because the triangles satisfy the AAS triangle congruence criterion. (Yes or No)

Triangles ABC and ADC are congruent because the triangles satisfy the ASA triangle congruence criterion. (Yes or No)

Triangles ABC and ADC are congruent
because there is a rotation that will carry one triangle onto the other. (Yes or No)

Triangles ABC and ADC are congruent because there is a reflection that will carry one triangle onto the other. (Yes or No)

Triangles ABC and ADC are congruent because there is a translation that will carry one triangle onto the other (Yes or No)

Triangles ABC and ADC are congruent based on the ASA congruence theorem, and by reflection, one triangle can be carried onto the other triangle, therefore:

Statement 1 is NO
Statement 2 is YES
Statement 3 is NO
Statement 4 is YES
Statement 5 is NO

Recall:

The diagram shows the congruence theorem that can prove that two triangles are congruent.

Two triangles that are reflection of each other can also be said to be congruent triangles.

Thus:

The image of both triangles given shows that they have two pairs of angles and an included side, which means that the ASA Congruence Theorem can be used to prove their congruency. Therefore,

Statement 1 is NO
Statement 2 is YES.

Also, the transformation that can justify that triangles ABC and ADC are congruent is reflection that will carry one triangle onto the other triangle.

Therefore,

Statement 4 is YES
Statement 3 and 5 is NO.

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