Worksheet for practicing SSS triangle congruence proofs with diagrams and logical steps.

Problem Analysis:

The task involves solving problems related to Side-Side-Side (SSS) Triangle Congruence using the given diagrams and information. The SSS Congruence Theorem states that if three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent.

We will solve each part step by step:

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Part 1:

#### Given:
- \( \triangle ABC \cong \triangle DEF \)
- \( AB = DE \), \( BC = EF \), \( AC = DF \)

#### Task:
Determine if the following statements are true or false based on the given congruence.

1. \( \angle A \cong \angle D \)
2. \( \angle B \cong \angle E \)
3. \( \angle C \cong \angle F \)

#### Solution:
Since \( \triangle ABC \cong \triangle DEF \), all corresponding parts of the triangles are congruent. This includes both sides and angles. Therefore:
- \( \angle A \cong \angle D \)
- \( \angle B \cong \angle E \)
- \( \angle C \cong \angle F \)

#### Reasoning:
By the definition of congruent triangles, if two triangles are congruent, their corresponding angles are also congruent.

#### Final Answer for Part 1:
\[
\boxed{\text{True, True, True}}
\]

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Part 2:

#### Given:
- \( \triangle XYZ \cong \triangle XZY \)
- \( XY = XZ \), \( YZ = ZY \), \( XZ = ZX \)

#### Task:
Determine if the following statements are true or false based on the given congruence.

1. \( \angle X \cong \angle X \)
2. \( \angle Y \cong \angle Z \)
3. \( \triangle XYZ \cong \triangle XZY \)

#### Solution:
1. \( \angle X \cong \angle X \): This is trivially true because any angle is congruent to itself.
2. \( \angle Y \cong \angle Z \): Since \( \triangle XYZ \cong \triangle XZY \), corresponding angles must be congruent. Here, \( \angle Y \) in \( \triangle XYZ \) corresponds to \( \angle Z \) in \( \triangle XZY \), so \( \angle Y \cong \angle Z \).
3. \( \triangle XYZ \cong \triangle XZY \): This is given in the problem statement, so it is true.

#### Final Answer for Part 2:
\[
\boxed{\text{True, True, True}}
\]

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Part 3:

#### Given:
- \( \triangle LMN \cong \triangle LNM \)
- \( LM = LN \), \( MN = NM \), \( LN = ML \)

#### Task:
Determine if the following statements are true or false based on the given congruence.

1. \( \angle L \cong \angle L \)
2. \( \angle M \cong \angle N \)
3. \( \triangle LMN \cong \triangle LNM \)

#### Solution:
1. \( \angle L \cong \angle L \): This is trivially true because any angle is congruent to itself.
2. \( \angle M \cong \angle N \): Since \( \triangle LMN \cong \triangle LNM \), corresponding angles must be congruent. Here, \( \angle M \) in \( \triangle LMN \) corresponds to \( \angle N \) in \( \triangle LNM \), so \( \angle M \cong \angle N \).
3. \( \triangle LMN \cong \triangle LNM \): This is given in the problem statement, so it is true.

#### Final Answer for Part 3:
\[
\boxed{\text{True, True, True}}
\]

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Final Summary:

For all three parts, the answers are:
\[
\boxed{\text{True, True, True}}
\]