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Based on the image provided, it appears you need to fill in the proof table for exercises 16 to 18. I'll guide you through creating the proof table for each exercise.

### Exercise 16 Proof Table
- **Given:** \(\triangle\) LMP, \(\overline{LM} \cong \overline{LP}\)
- **To Prove:** \(\angle M \cong \angle P\)

| Statements                                | Reasons                        |
|-------------------------------------------|--------------------------------|
| 1. \(\overline{LM} \cong \overline{LP}\)  | Given                          |
| 2. \(\angle LMP = \angle LPM\)            | Isosceles Triangle Theorem     |
| 3. \(\angle M \cong \angle P\)            | Definition of congruent angles |

### Exercise 17 Proof Table
- **Given:** \(\overline{AB} \cong \overline{AC}\), \(\overline{BD} \cong \overline{CD}\)
- **To Prove:** \(\overline{AD}\) bisects \(\angle BAC\)

| Statements                                | Reasons                        |
|-------------------------------------------|--------------------------------|
| 1. \(\overline{AB} \cong \overline{AC}\)  | Given                          |
| 2. \(\overline{BD} \cong \overline{CD}\)  | Given                          |
| 3. \(\angle ABD \cong \angle ACD\)        | Isosceles Triangle Theorem     |
| 4. \(\overline{AD}\) bisects \(\angle BAC\) | Definition of angle bisector |

### Exercise 18 Proof Table
- **Given:** \(\overline{DE} \cong \overline{FE}\), \(\overline{DE} \perp \overline{DF}\)
- **To Prove:** \(\overline{DF}\) bisects \(\angle DEF\)

| Statements                                | Reasons                        |
|-------------------------------------------|--------------------------------|
| 1. \(\overline{DE} \cong \overline{FE}\)  | Given                          |
| 2. \(\overline{DE} \perp \overline{DF}\)  | Given                          |
| 3. \(\overline{DF}\) bisects \(\angle DEF\) | Definition of perpendicular bisector |

Would you like more detailed explanations, or do you have any questions?

Here are some related questions to expand your understanding:
1. What is the Isosceles Triangle Theorem?
2. How can you prove that a line bisects an angle?
3. Why is the perpendicular bisector significant in a triangle?
4. What other properties can you infer if two sides of a triangle are congruent?
5. How can the congruence of angles help in solving geometric proofs?

**Tip:** Always start with the given information when proving a statement, as it helps to establish the foundation for your reasoning.

Explore proof tables for geometry exercises 16 to 18 focusing on isosceles triangles and angle bisectors. Each exercise includes step-by-step reasoning using key theorems like the Isosceles Triangle Theorem and Angle Bisector Theorem. Suitable for high school geometry students.

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