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

### Find the measure of each angle in the diagram.

Vertical angles are formed when two lines meet each other at a point. They are always equal to each other. In other words, whenever two lines cross or intersect each other, 4 angles are formed. We can observe that two angles that are opposite to each other are equal and they are called vertical angles.

### Find the measure of each angle in the diagram.

Vertical angles are formed when two lines meet each other at a point. They are always equal to each other. In other words, whenever two lines cross or intersect each other, 4 angles are formed. We can observe that two angles that are opposite to each other are equal and they are called vertical angles.

### 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.

Two angles are said to be supplementary is the sum of their measures 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.

Two angles are said to be supplementary is the sum of their measures 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.

### 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 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.

### 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.

Here, sum of angles 1 and 2 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.

Here, sum of angles 1 and 2 is 180°.

### 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 | ||

2 | ||

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°.