Question

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

aas
asa
sas
not congruent

Explanation:

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<reasoning>

Identify given congruent parts

Using the Triangle Congruence Postulates knowledge point
\[

$$\begin{aligned} &\angle A_1 \cong \angle A_2 \quad \text{(marked acute angles)}\\ &\angle R_1 \cong \angle R_2 \quad \text{(marked right angles)}\\ &S_1 \cong S_2 \quad \text{(marked vertical segments)} \end{aligned}$$

\]

Determine the congruence pattern

The marked parts consist of two angles and a non-included side (AAS).

Select the correct postulate

The AAS (Angle-Angle-Side) theorem proves congruence.
</reasoning>

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

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Answer:

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<reasoning>

Identify given congruent parts

Using the Triangle Congruence Postulates knowledge point
\[

$$\begin{aligned} &\angle A_1 \cong \angle A_2 \quad \text{(marked acute angles)}\\ &\angle R_1 \cong \angle R_2 \quad \text{(marked right angles)}\\ &S_1 \cong S_2 \quad \text{(marked vertical segments)} \end{aligned}$$

\]

Determine the congruence pattern

The marked parts consist of two angles and a non-included side (AAS).

Select the correct postulate

The AAS (Angle-Angle-Side) theorem proves congruence.
</reasoning>

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

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