39. fill in the missing statements and reasons to complete the following proof.
given: $\overline{bd}$ and $\overline{ac}$ bisect each other at point $e$
prove: $\triangle bea \cong \triangle dec$
image of a quadrilateral with points b, c, d, a and intersection e of diagonals bd and ac
| statements | reasons |
| --- | --- |
| 1. $\overline{bd}$ and $\overline{ac}$ bisect each other at point $e$ | 1. |
| 2. $be = ed$ and $ae = ec$ | 2. |
| 3. | 3. definition of congruence |
| 4. $\angle bea \cong \angle dec$ | 4. |
| 5. | 5. |

Question

39. fill in the missing statements and reasons to complete the following proof.
given: $\overline{bd}$ and $\overline{ac}$ bisect each other at point $e$
prove: $\triangle bea \cong \triangle dec$
image of a quadrilateral with points b, c, d, a and intersection e of diagonals bd and ac
| statements | reasons |
| --- | --- |
| 1. $\overline{bd}$ and $\overline{ac}$ bisect each other at point $e$ | 1.  |
| 2. $be = ed$ and $ae = ec$ | 2.  |
| 3.  | 3. definition of congruence |
| 4. $\angle bea \cong \angle dec$ | 4.  |
| 5.  | 5.  |

Accepted Answer

# Explanation:
## Step1: Identify Reason for Statement 1
The first statement is given, so the reason is "Given".
## Step2: Reason for Statement 2
Since $ \overline{BD} $ and $ \overline{AC} $ bisect each other at $ E $, by the definition of a bisector (a bisector divides a segment into two equal parts), we get $ BE = ED $ and $ AE = EC $. So the reason is "Definition of Bisector".
## Step3: Statement for Reason 3
The reason is "Definition of Congruence", which states that if two segments have equal length, they are congruent. So from $ BE = ED $ and $ AE = EC $, we can write $ \overline{BE} \cong \overline{ED} $ and $ \overline{AE} \cong \overline{EC} $.
## Step4: Reason for Statement 4
$ \angle BEA $ and $ \angle DEC $ are vertical angles. Vertical angles are congruent, so the reason is "Vertical Angles Theorem".
## Step5: Statement and Reason for Step 5
To prove $ \triangle BEA \cong \triangle DEC $, we have $ \overline{BE} \cong \overline{ED} $, $ \overline{AE} \cong \overline{EC} $, and $ \angle BEA \cong \angle DEC $. This satisfies the SAS (Side - Angle - Side) Congruence Postulate. So the statement is $ \triangle BEA \cong \triangle DEC $ and the reason is "SAS Congruence Postulate".

# Answer:
1. Reason for Statement 1: Given
2. Reason for Statement 2: Definition of Bisector
3. Statement for Reason 3: $ \overline{BE} \cong \overline{ED} $ and $ \overline{AE} \cong \overline{EC} $
4. Reason for Statement 4: Vertical Angles Theorem
5. Statement for Reason 5: $ \triangle BEA \cong \triangle DEC $; Reason for Statement 5: SAS Congruence Postulate

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QUESTION IMAGE

Question

Explanation:

Step1: Identify Reason for Statement 1

Step2: Reason for Statement 2

Step3: Statement for Reason 3

Step4: Reason for Statement 4

Step5: Statement and Reason for Step 5

Answer:

statements	reasons
2. \\(be = ed\\) and \\(ae = ec\\)	2.
3.	3. definition of congruence
4. \\(\angle bea \cong \angle dec\\)	4.
5.	5.