Question

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

aas

sss

asa

sas

not congruent

Explanation:

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<reasoning>

Identify the given congruent parts

We analyze the markings on the two triangles sharing a common side.

• One pair of sides has single tick marks, indicating they are congruent.
• One pair of angles has single arc marks, indicating they are congruent.

Identify the shared side

Using the Triangle Congruence Postulates, we look for additional shared elements.

• The two triangles share a common diagonal side.
• By the Reflexive Property of Congruence, this shared side is congruent to itself.

Determine the congruence postulate

We evaluate the relative positions of the known congruent parts:

• We have a congruent side (tick mark).
• We have a congruent angle (arc mark).
• We have the shared side.
• The congruent angle is located between the marked side and the shared side.
• This configuration corresponds to the Side-Angle-Side (SAS Congruence) postulate.

</reasoning>

<answer>
<mcq-option>AAS</mcq-option>
<mcq-option>SSS</mcq-option>
<mcq-option>ASA</mcq-option>
<mcq-correct>SAS</mcq-correct>
<mcq-option>not congruent</mcq-option>
</answer>

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Answer:

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<reasoning>

Identify the given congruent parts

We analyze the markings on the two triangles sharing a common side.

• One pair of sides has single tick marks, indicating they are congruent.
• One pair of angles has single arc marks, indicating they are congruent.

Identify the shared side

Using the Triangle Congruence Postulates, we look for additional shared elements.

• The two triangles share a common diagonal side.
• By the Reflexive Property of Congruence, this shared side is congruent to itself.

Determine the congruence postulate

We evaluate the relative positions of the known congruent parts:

• We have a congruent side (tick mark).
• We have a congruent angle (arc mark).
• We have the shared side.
• The congruent angle is located between the marked side and the shared side.
• This configuration corresponds to the Side-Angle-Side (SAS Congruence) postulate.

</reasoning>

<answer>
<mcq-option>AAS</mcq-option>
<mcq-option>SSS</mcq-option>
<mcq-option>ASA</mcq-option>
<mcq-correct>SAS</mcq-correct>
<mcq-option>not congruent</mcq-option>
</answer>

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