Mathematics
Grade9
Easy
Question
The steps of a proof are shown.
Given: T is the midpoint of 
.
Prove: x = 5
What is reason 4?
| Statements | Reasons |
1. T is the midpoint of  |
1. Given |
2.  |
|
| 3. ST = TU | |
| 4. 7x = 3x + 20 | |
| 5. 4x = 20 | |
| 6. x = 5 |
- Definition of midpoint
- Division Property of Equality
- Substitution Property of Equality
- Definition of congruent segments
Hint:
The correct answer is: Substitution Property of Equality
The whole proof:
Statements
Reasons
1. T is the midpoint of
1. Given
2.
2. Definition of midpoint
3. ST = TU
3. Definition of congruent segments
4. 7x = 3x + 20
4. Substitution Property of Equality
5. 4x = 20
5. Subtraction Property of Equality
6. x = 5
6. Division Property of Equality
In this question, we have to find the reason for 4. As congruent line segments are defined as line segments which are equal in length, the division property of equality states that dividing both sides of an equation by the same number does not affect the equation, the substitution property of equality allows equal quantities to replace each other at any time in any math sentence and a midpoint is a point on a line segment that divides it into two equal parts.
