10 given: $\overline{km} \cong \overline{nm}$, $\overline{lk} \cong \overline{ln}$ prove: $\triangle lkm \cong \triangle lnm$ $\begin{array}{|c|c|} \hline \text{statements} & \text{reasons} \\ \hline 1. & 1. \\ \hline 2. & 2. \\ \hline 3. & 3. \\ \hline 4. & 4. \\ \hline \end{array}$ 11 given: $\overline{ad} \cong \overline{ab}$, $\overline{ac}$ bisects $\angle dab$ prove: $\triangle adc \cong \triangle abc$ $\begin{array}{|c|c|} \hline \text{statements} & \text{reasons} \\ \hline 1. & 1. \\ \hline 2. & 2. \\ \hline 3. & 3. \\ \hline 4. & 4. \\ \hline 5. & 5. \\ \hline \end{array}$ 12 given: $\overline{jm} \cong \overline{nm}$, $l$ is the midpoint of $\overline{jn}$ prove: $\triangle jlm \cong \triangle nlm$ $\begin{array}{|c|c|} \hline \text{statements} & \text{reasons} \\ \hline 1. & 1. \\ \hline 2. & 2. \\ \hline 3. & 3. \\ \hline 4. & 4. \\ \hline 5. & 5. \\ \hline \end{array}$

Question

Accepted Answer

### Problem 10 (Proving $	riangle LKM \cong 	riangle LNM$)
# Explanation:
## Step 1: List Given Information
- Statement 1: $\overline{KM} \cong \overline{NM}$ (Given)
- Statement 2: $\overline{LK} \cong \overline{LN}$ (Given)
- Statement 3: $\overline{LM} \cong \overline{LM}$ (Reflexive Property of Congruence)
## Step 2: Apply SSS Congruence
- Statement 4: $	riangle LKM \cong 	riangle LNM$ (SSS Congruence Postulate, since all three corresponding sides are congruent)
- Reasons:
  1. Given
  2. Given
  3. Reflexive Property
  4. SSS Congruence Postulate

### Problem 11 (Proving $	riangle ADC \cong 	riangle ABC$)
# Explanation:
## Step 1: List Given Information
- Statement 1: $\overline{AD} \cong \overline{AB}$ (Given)
- Statement 2: $\overline{AC}$ bisects $\angle DAB$ (Given), so $\angle DAC \cong \angle BAC$ (Definition of Angle Bisector)
- Statement 3: $\overline{AC} \cong \overline{AC}$ (Reflexive Property of Congruence)
## Step 2: Apply SAS Congruence
- Statement 4: $	riangle ADC \cong 	riangle ABC$ (SAS Congruence Postulate, since two sides and the included angle are congruent)
- Reasons:
  1. Given
  2. Given; Definition of Angle Bisector
  3. Reflexive Property
  4. SAS Congruence Postulate

### Problem 12 (Proving $	riangle JLM \cong 	riangle NLM$)
# Explanation:
## Step 1: List Given Information
- Statement 1: $\overline{JM} \cong \overline{NM}$ (Given)
- Statement 2: $L$ is the midpoint of $\overline{JN}$, so $\overline{JL} \cong \overline{LN}$ (Definition of Midpoint)
- Statement 3: $\overline{LM} \cong \overline{LM}$ (Reflexive Property of Congruence)
## Step 2: Apply SSS Congruence
- Statement 4: $	riangle JLM \cong 	riangle NLM$ (SSS Congruence Postulate, since all three corresponding sides are congruent)
- Reasons:
  1. Given
  2. Given; Definition of Midpoint
  3. Reflexive Property
  4. SSS Congruence Postulate

# Answer (for each problem's proof table):

### Problem 10 Table:
| Statements | Reasons |
| --- | --- |
| 1. $\overline{KM} \cong \overline{NM}$ | 1. Given |
| 2. $\overline{LK} \cong \overline{LN}$ | 2. Given |
| 3. $\overline{LM} \cong \overline{LM}$ | 3. Reflexive Property |
| 4. $	riangle LKM \cong 	riangle LNM$ | 4. SSS Congruence Postulate |

### Problem 11 Table:
| Statements | Reasons |
| --- | --- |
| 1. $\overline{AD} \cong \overline{AB}$ | 1. Given |
| 2. $\angle DAC \cong \angle BAC$ | 2. Given ( $\overline{AC}$ bisects $\angle DAB$ ); Definition of Angle Bisector |
| 3. $\overline{AC} \cong \overline{AC}$ | 3. Reflexive Property |
| 4. $	riangle ADC \cong 	riangle ABC$ | 4. SAS Congruence Postulate |

### Problem 12 Table:
| Statements | Reasons |
| --- | --- |
| 1. $\overline{JM} \cong \overline{NM}$ | 1. Given |
| 2. $\overline{JL} \cong \overline{LN}$ | 2. Given ( $L$ is midpoint of $\overline{JN}$ ); Definition of Midpoint |
| 3. $\overline{LM} \cong \overline{LM}$ | 3. Reflexive Property |
| 4. $	riangle JLM \cong 	riangle NLM$ | 4. SSS Congruence Postulate |

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QUESTION IMAGE

Question

Explanation:

Problem 10 (Proving $\triangle LKM \cong \triangle LNM$)

Step 1: List Given Information

Step 2: Apply SSS Congruence

Problem 11 (Proving $\triangle ADC \cong \triangle ABC$)

Step 1: List Given Information

Step 2: Apply SAS Congruence

Problem 12 (Proving $\triangle JLM \cong \triangle NLM$)

Step 1: List Given Information

Step 2: Apply SSS Congruence

Answer:

Problem 10 Table:

Problem 11 Table:

Problem 12 Table:

Statements	Reasons
2. $\overline{LK} \cong \overline{LN}$	2. Given
3. $\overline{LM} \cong \overline{LM}$	3. Reflexive Property
4. $\triangle LKM \cong \triangle LNM$	4. SSS Congruence Postulate

Statements	Reasons
2. $\angle DAC \cong \angle BAC$	2. Given ( $\overline{AC}$ bisects $\angle DAB$ ); Definition of Angle Bisector
3. $\overline{AC} \cong \overline{AC}$	3. Reflexive Property
4. $\triangle ADC \cong \triangle ABC$	4. SAS Congruence Postulate

Statements	Reasons
2. $\overline{JL} \cong \overline{LN}$	2. Given ( $L$ is midpoint of $\overline{JN}$ ); Definition of Midpoint
3. $\overline{LM} \cong \overline{LM}$	3. Reflexive Property
4. $\triangle JLM \cong \triangle NLM$	4. SSS Congruence Postulate