Question
Give the reason for statement #4.
Given: PS = RT, PQ = ST
Prove: QS = RS
| Statement | Reason |
| 1. PS = RT, PQ = ST |
1. |
| 2. PQ + QS = PS |
2. |
| 3. ST + QS = RT |
3. |
| 4. RS + ST = RT |
4. |
| 5. ST + QS = RS + ST |
5. |
| 6. QS = RS |
6. |
- Reflexive property
- Addition of equality
- Substitution
- Segment Addition Postulate
Hint:
Segment Addition Postulate .
The correct answer is: Segment Addition Postulate
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.
So , RS + ST = RT holds .
Geometrically, a line segment with three collinear points is subject to the segment addition postulate. By the segment addition postulate, point B will only be on the same line segment as points A and C if the sum of AB and BC equals AC if there are two given points on the segment between them, A and C. According to the segment addition postulate, if a line segment has endpoints A and C, and a third point B, then only if the equation AB + BC = AC is true does the third point B lie on the line segment AC. To further comprehend this postulate, look at the illustration provided below.
Related Questions to study
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Two lines that are not perpendicular intersect such that ∠1 and ∠2 are a linear pair, ∠1 and ∠4 are a linear pair, and ∠1 and ∠3 are vertical angles. Tell whether the following statement is true or false.
The sum of the angles of a linear pair is 180°.
Two lines that are not perpendicular intersect such that ∠1 and ∠2 are a linear pair, ∠1 and ∠4 are a linear pair, and ∠1 and ∠3 are vertical angles. Tell whether the following statement is true or false.
The sum of the angles of linear pair is 180°.
Two lines that are not perpendicular intersect such that ∠1 and ∠2 are a linear pair, ∠1 and ∠4 are a linear pair, and ∠1 and ∠3 are vertical angles. Tell whether the following statement is true or false.
The sum of the angles of linear pair is 180°.
Two lines that are not perpendicular intersect such that ∠1 and ∠2 are a linear pair, ∠1 and ∠4 are a linear pair, and ∠1 and ∠3 are vertical angles. Tell whether the following statement is true or false.
Vertical angles are always equal.
Two lines that are not perpendicular intersect such that ∠1 and ∠2 are a linear pair, ∠1 and ∠4 are a linear pair, and ∠1 and ∠3 are vertical angles. Tell whether the following statement is true or false.
Vertical angles are always equal.
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Here, sum of angles 1 and 2 is 180°.
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Which property does the statement illustrate?
Same applies on number and shapes.
Which property does the statement illustrate?
Same applies on number and shapes.
Which property does the statement illustrate?
If a=b, then b = a.
Which property does the statement illustrate?
If a=b, then b = a.
Find the measure of each angle in the diagram.
Find the measure of each angle in the diagram.
Complete the statement with <, >, or =.
If m∠ 4 = 30, then m∠ 5? m∠ 4.
When two angles are formed on a straight line, they are called linear pair.
Complete the statement with <, >, or =.
If m∠ 4 = 30, then m∠ 5? m∠ 4.
When two angles are formed on a straight line, they are called linear pair.
Complete the statement with <, >, or =.
m∠ 8 + m∠ 6? 150
When two angles are formed on a straight line, they are called linear pair.
Complete the statement with <, >, or =.
m∠ 8 + m∠ 6? 150
When two angles are formed on a straight line, they are called linear pair.
What is the reason for statement 2?
| Statement | Reason | |
| 1 |  |
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| 2 |  |
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| 3 |  |
Alternate exterior angles are always equal.
What is the reason for statement 2?
| Statement | Reason | |
| 1 | |
|
| 2 | |
|
| 3 | |
Alternate exterior angles are always equal.
What is the reason for statement 3?
| Statement | Reason | |
| 1 | |
|
| 2 | |
|
| 3 | |
Corresponding angles are equal.
What is the reason for statement 3?
| Statement | Reason | |
| 1 | |
|
| 2 | |
|
| 3 | |
Corresponding angles are equal.
Solve for x.
In math, a linear pair of angles are those two adjacent angles whose sum is 180°.
Solve for x.
In math, a linear pair of angles are those two adjacent angles whose sum is 180°.
