Question

if the two triangles are congruent, state how you know. if not, state
ot congruent.\

asa
aas
sas
sss
not congruent

Explanation:

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<reasoning>

Identify the given congruent sides

Using the Triangle Congruence Postulates knowledge point

• One pair of corresponding sides has double tick marks, indicating they are congruent.
• Another pair of corresponding sides has triple tick marks, indicating they are congruent.

Identify the vertical angles

Using the Vertical Angles Theorem knowledge point

• The two triangles share a vertex where their lines intersect.
• The angles opposite each other at this intersection are vertical angles, which are congruent.

Apply the congruence postulate

Using the SAS Congruence knowledge point

• The congruent vertical angles are located directly between the two pairs of congruent sides.
• This Side-Angle-Side relationship proves the two triangles are congruent.

</reasoning>

<answer>
<mcq-option>(A) ASA</mcq-option>
<mcq-option>(B) AAS</mcq-option>
<mcq-correct>(C) SAS</mcq-correct>
<mcq-option>(D) SSS</mcq-option>
<mcq-option>(E) not congruent</mcq-option>
</answer>

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Answer:

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<reasoning>

Identify the given congruent sides

Using the Triangle Congruence Postulates knowledge point

• One pair of corresponding sides has double tick marks, indicating they are congruent.
• Another pair of corresponding sides has triple tick marks, indicating they are congruent.

Identify the vertical angles

Using the Vertical Angles Theorem knowledge point

• The two triangles share a vertex where their lines intersect.
• The angles opposite each other at this intersection are vertical angles, which are congruent.

Apply the congruence postulate

Using the SAS Congruence knowledge point

• The congruent vertical angles are located directly between the two pairs of congruent sides.
• This Side-Angle-Side relationship proves the two triangles are congruent.

</reasoning>

<answer>
<mcq-option>(A) ASA</mcq-option>
<mcq-option>(B) AAS</mcq-option>
<mcq-correct>(C) SAS</mcq-correct>
<mcq-option>(D) SSS</mcq-option>
<mcq-option>(E) not congruent</mcq-option>
</answer>

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