Question

11 multiple choice 1 point

\\(\delta jar \cong \delta \\_\\)

dli aas
dli by sss
dil by sss
dil by aas

Explanation:

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<reasoning>

Identify corresponding congruent parts

We analyze the markings on \(\Delta JAR\) and the second triangle:

• Side \(JR\) has a single tick mark, which corresponds to side \(LD\) with a single tick mark: \(JR \cong LD\).
• Angle \(\angle R\) has a single arc mark, which corresponds to angle \(\angle L\) with a single arc mark: \(\angle R \cong \angle L\).
• Angle \(\angle A\) has a double arc mark with a tick, which corresponds to angle \(\angle I\) with a double arc mark with a tick: \(\angle A \cong \angle I\).

Determine the congruence postulate

Using the Triangle Congruence Postulates, we observe the relative positions of the congruent parts:

• We have two angles and a non-included side congruent to the corresponding two angles and non-included side of the other triangle.
• This matches the AAS Congruence theorem (Angle-Angle-Side).

Match corresponding vertices

To write the correct triangle congruence statement \(\Delta JAR \cong \Delta \_\_\_\):

• Vertex \(J\) corresponds to vertex \(D\) (the vertex opposite the angle with the double-arc-tick mark).
• Vertex \(A\) corresponds to vertex \(I\) (since \(\angle A \cong \angle I\)).
• Vertex \(R\) corresponds to vertex \(L\) (since \(\angle R \cong \angle L\)).

Therefore, \(\Delta JAR \cong \Delta DIL\) by AAS Congruence.
</reasoning>

<answer>
<mcq-option>DLI AAS</mcq-option>
<mcq-option>DLI by SSS</mcq-option>
<mcq-option>DIL by SSS</mcq-option>
<mcq-correct>DIL by AAS</mcq-correct>
</answer>

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Answer:

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<reasoning>

Identify corresponding congruent parts

We analyze the markings on \(\Delta JAR\) and the second triangle:

• Side \(JR\) has a single tick mark, which corresponds to side \(LD\) with a single tick mark: \(JR \cong LD\).
• Angle \(\angle R\) has a single arc mark, which corresponds to angle \(\angle L\) with a single arc mark: \(\angle R \cong \angle L\).
• Angle \(\angle A\) has a double arc mark with a tick, which corresponds to angle \(\angle I\) with a double arc mark with a tick: \(\angle A \cong \angle I\).

Determine the congruence postulate

Using the Triangle Congruence Postulates, we observe the relative positions of the congruent parts:

• We have two angles and a non-included side congruent to the corresponding two angles and non-included side of the other triangle.
• This matches the AAS Congruence theorem (Angle-Angle-Side).

Match corresponding vertices

To write the correct triangle congruence statement \(\Delta JAR \cong \Delta \_\_\_\):

• Vertex \(J\) corresponds to vertex \(D\) (the vertex opposite the angle with the double-arc-tick mark).
• Vertex \(A\) corresponds to vertex \(I\) (since \(\angle A \cong \angle I\)).
• Vertex \(R\) corresponds to vertex \(L\) (since \(\angle R \cong \angle L\)).

Therefore, \(\Delta JAR \cong \Delta DIL\) by AAS Congruence.
</reasoning>

<answer>
<mcq-option>DLI AAS</mcq-option>
<mcq-option>DLI by SSS</mcq-option>
<mcq-option>DIL by SSS</mcq-option>
<mcq-correct>DIL by AAS</mcq-correct>
</answer>

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