Question

state what postulate proves that the two triangles are congruent. if not congruent, state not congruent.

sas
asa
aas
not congruent

Explanation:

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<reasoning>

Analyze the markings on the first triangle

The first triangle has:

• A side marked with two tick marks.
• An adjacent angle marked with an arc.
• A side marked with three tick marks adjacent to that angle.

This represents a Side-Angle-Side (SAS) configuration where the angle is included between the two marked sides.

Analyze the markings on the second triangle

The second triangle has:

• A side marked with two tick marks.
• An angle marked with an arc that is NOT between the two marked sides.
• A side marked with three tick marks.

This represents a Side-Side-Angle (SSA) configuration.

Compare the configurations

For two triangles to be congruent by a postulate, their corresponding marked parts must match the same postulate structure.

• The first triangle has the marked angle included between the two marked sides (SAS).
• The second triangle has the marked angle opposite to one of the marked sides (SSA).
• Since the corresponding parts do not share the same relative positions, we cannot prove congruence.
• Furthermore, SSA (Side-Side-Angle) is not a valid congruence postulate.

Determine the final conclusion

Because the marked parts do not correspond in a way that satisfies any valid congruence postulate (such as SAS, ASA, AAS, or SSS), the triangles cannot be proven congruent.
Thus, the correct choice is "Not congruent".
</reasoning>

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

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Answer:

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<reasoning>

Analyze the markings on the first triangle

The first triangle has:

• A side marked with two tick marks.
• An adjacent angle marked with an arc.
• A side marked with three tick marks adjacent to that angle.

This represents a Side-Angle-Side (SAS) configuration where the angle is included between the two marked sides.

Analyze the markings on the second triangle

The second triangle has:

• A side marked with two tick marks.
• An angle marked with an arc that is NOT between the two marked sides.
• A side marked with three tick marks.

This represents a Side-Side-Angle (SSA) configuration.

Compare the configurations

For two triangles to be congruent by a postulate, their corresponding marked parts must match the same postulate structure.

• The first triangle has the marked angle included between the two marked sides (SAS).
• The second triangle has the marked angle opposite to one of the marked sides (SSA).
• Since the corresponding parts do not share the same relative positions, we cannot prove congruence.
• Furthermore, SSA (Side-Side-Angle) is not a valid congruence postulate.

Determine the final conclusion

Because the marked parts do not correspond in a way that satisfies any valid congruence postulate (such as SAS, ASA, AAS, or SSS), the triangles cannot be proven congruent.
Thus, the correct choice is "Not congruent".
</reasoning>

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

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