Sign In
If M is the midpoint of AB, then AB=2AM. |
In the first row, write the given statement in the left-hand side column. This statement is given, not derived, so write given in the right-hand column.
0. Statements
|
0. Reasons
|
1. M is the midpoint of AB
|
1. Given
|
If possible, draw a diagram that helps to derive the information that will be written in the table. This diagram will not be included in the table, though.
0. Statements
|
0. Reasons
|
1. M is the midpoint of AB
|
1. Given
|
2. MB=AM
|
2. Definition of Midpoint
|
The statements written so far are not enough to reach to the desired conclusion, so continue deriving information and combining it until it points to the desired statement. Remember that postulates, theorems, or other mathematical reasoning can be used.
0. Statements
|
0. Reasons
|
1. M is the midpoint of AB
|
1. Given
|
2. MB=AM
|
2. Definition of Midpoint
|
0. Statements
|
0. Reasons
|
1. M is the midpoint of AB
|
1. Given
|
2. MB=AM
|
2. Definition of Midpoint
|
3. AB=AM+MB
|
3. Segment Addition Postulate
|
Next, use the Substitution Property of Equality to substitute the equation written in the second row into the equation written in the third row.
0. Statements
|
0. Reasons
|
1. M is the midpoint of AB
|
1. Given
|
2. MB=AM
|
2. Definition of Midpoint
|
3. AB=AM+MB
|
3. Segment Addition Postulate
|
4. AB=AM+AM
|
4. Substitution Property of Equality
|
The right-hand side of the last equation can be simplified by adding the two terms.
0. Statements
|
0. Reasons
|
1. M is the midpoint of AB
|
1. Given
|
2. MB=AM
|
2. Definition of Midpoint
|
3. AB=AM+MB
|
3. Segment Addition Postulate
|
4. AB=AM+AM
|
4. Substitution Property of Equality
|
5. AB=2AM
|
5. Simplify
|
Notice that the last statement is the desired one. Therefore, the proof is done!