Question

complete the following congruency statement based on the following triangle by dragging the letters to their correct positions:

\\(\delta cab \cong \delta\\)

Explanation:

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<reasoning>

Identify corresponding congruent parts

Using the markings on the triangles:

• Side \(AB\) has a single tick mark, and side \(ED\) has a single tick mark, so \(AB \cong ED\).
• Side \(BC\) has a double tick mark, and side \(DC\) has a double tick mark, so \(BC \cong DC\).
• Angle \(\angle B\) has an arc marking, and angle \(\angle D\) has an arc marking, so \(\angle B \cong \angle D\).

Match corresponding vertices

Based on the congruent sides and angles:

• Vertex \(B\) corresponds to vertex \(D\) (since \(\angle B \cong \angle D\)).
• Since \(BC \cong DC\) and \(B\) corresponds to \(D\), vertex \(C\) of \(\triangle CAB\) corresponds to vertex \(C\) of \(\triangle CED\).
• Since \(AB \cong ED\) and \(B\) corresponds to \(D\), vertex \(A\) corresponds to vertex \(E\).

Determine the congruence statement

The given statement starts with \(\triangle CAB\). Matching each vertex in order:

• \(C

ightarrow C\)

• \(A

ightarrow E\)

• \(B

ightarrow D\)

Therefore, \(\triangle CAB \cong \triangle CED\).
</reasoning>

<answer>
Complete the following congruency statement based on the following triangle by dragging the letters to their correct positions:

\(\triangle CAB \cong \triangle\) <blank>\(CED\)</blank>
</answer>

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"Mathematics",
"Geometry",
"Triangle Congruence Correspondence"
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</post_analysis>

Answer:

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<reasoning>

Identify corresponding congruent parts

Using the markings on the triangles:

• Side \(AB\) has a single tick mark, and side \(ED\) has a single tick mark, so \(AB \cong ED\).
• Side \(BC\) has a double tick mark, and side \(DC\) has a double tick mark, so \(BC \cong DC\).
• Angle \(\angle B\) has an arc marking, and angle \(\angle D\) has an arc marking, so \(\angle B \cong \angle D\).

Match corresponding vertices

Based on the congruent sides and angles:

• Vertex \(B\) corresponds to vertex \(D\) (since \(\angle B \cong \angle D\)).
• Since \(BC \cong DC\) and \(B\) corresponds to \(D\), vertex \(C\) of \(\triangle CAB\) corresponds to vertex \(C\) of \(\triangle CED\).
• Since \(AB \cong ED\) and \(B\) corresponds to \(D\), vertex \(A\) corresponds to vertex \(E\).

Determine the congruence statement

The given statement starts with \(\triangle CAB\). Matching each vertex in order:

• \(C

ightarrow C\)

• \(A

ightarrow E\)

• \(B

ightarrow D\)

Therefore, \(\triangle CAB \cong \triangle CED\).
</reasoning>

<answer>
Complete the following congruency statement based on the following triangle by dragging the letters to their correct positions:

\(\triangle CAB \cong \triangle\) <blank>\(CED\)</blank>
</answer>

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