a diagram is shown where k i and m is a transversal. move statements and reasons to the table to prove that.
statements: trransitive property symmetric property vertical angles are congruent strait angles form a linear pair
1=2
2=3
3=5
3=4
1=4
Statements Reasons
1 = 2 Definition of congruent angles
2 = 3 Transitive property
3 = 5 Transitive property
1 = 4 Transitive property
3 = 4 Vertical angles are congruent
1 = 2 = 3 = 4 = 5 Symmetric property
1 and 5 form a linear pair Definition of a linear pair
To prove that 1=4, we need to provide a step-by-step logical sequence using the given statements and reasons. Here is how we can prove it:
| Step | Statement | Reason |
|--------------|----------------------------------------|----------------------------------------------------------|
| 1 | 1=2 | Transitive property |
| 2 | 2=3 | Transitive property |
| 3 | 3=5 | Transitive property |
| 4 | 3=4 | Transitive property |
| 5 | 1=3 | Substitution property (from step 1 and 2) |
| 6 | 1=4 | Transitive property (from step 5 and 4) |
Therefore, using the transitive property and the given statements, we have proven that 1=4.
To prove the given statement using the given properties, we can organize the statements and reasons in a two-column proof format:
| Statements | Reasons |
|------------------------------------------------|--------------------------------|
| 1 = 2 | Given |
| 2 = 3 | Given |
| 3 = 5 | Given |
| 3 = 4 | Given |
| 1 = 4 | Transitive Property |
| | |
| | |
Let's go through the steps and reasoning behind each statement:
1. 1 = 2: Given.
This is a given statement from the diagram.
2. 2 = 3: Given.
This is a given statement from the diagram.
3. 3 = 5: Given.
This is a given statement from the diagram.
4. 3 = 4: Given.
This is a given statement from the diagram.
5. 1 = 4: Transitive Property.
Since we have the statements 1 = 2, 2 = 3, 3 = 4, and 3 = 5, we can use the Transitive Property to conclude that 1 = 4. This property states that if a = b and b = c, then a = c.
All of the given statements have been used, and the Transitive Property has been applied to prove the final statement.