Mathematics
Grade9
Easy
Question
Four steps of a proof are shown.
Given: AC = AB + AB
Prove: AB = BC
What is step no. 2?
Statements
Reason
1. AC = AB + AB
1. Given
2. AB + BC = AC
3. AB + AB = AB + BC
4. AB = BC
| Statements | Reason |
| 1. AC = AB + AB | 1. Given |
| 2. AB + BC = AC | |
| 3. AB + AB = AB + BC | |
| 4. AB = BC |
- Substitution Property of Equality
- Transitive property
- Segment Addition Postulate
- Subtraction property of equality
Hint:
Segment Addition Postulate
The correct answer is: Segment Addition Postulate
Given for a line AB + BC = AC
The segment addition postulate in geometry is the axiom which states that a line segment divided into smaller pieces is the sum of the lengths of all those smaller segments. So, if we have three collinear points A, B, and C on segment AC, it means AB + BC = AC. It is a mathematical fact that can be accepted without proof.
Segment Addition postulate .
