UpStudy Free Solution:

To find the indicated lengths using the Segment Addition Postulate, we simply add the lengths of the segments provided.

6. Find \(MP\):

- \(MN = 5\)

- \(NP = 18\)

- Using the Segment Addition Postulate: \(MP = MN + NP\)

- \(MP = 5 + 18 = 23\)

7. Find \(RT\):

- \(RS = 22\)

- \(ST = 22\)

- Using the Segment Addition Postulate: \(RT = RS + ST\)

- \(RT = 22 + 22 = 44\)

8. Find \(UW\):

- \(UV = 39\)

- \(VW = 26\)

- Using the Segment Addition Postulate: \(UW = UV + VW\)

- \(UW = 39 + 26 = 65\)

So, the lengths are:

- \(MP = 23\)

- \(RT = 44\)

- \(UW = 65\)

Supplemental Knowledge

The Segment Addition Postulate is a fundamental concept in geometry that helps in determining the length of a line segment when given the lengths of its sub-segments. Here are some key points related to this topic:

1. Segment Addition Postulate:

- This postulate states that if a point \(B\) lies on the line segment \(AC\), then:

\[AB + BC = AC\]

- It implies that the total length of a segment is equal to the sum of the lengths of its parts.

2. Application in Problems:

- To find the length of a larger segment, you simply add the lengths of its smaller segments.

- This postulate is often used in conjunction with other geometric principles to solve more complex problems.

Gaining an understanding of fundamental concepts like the Segment Addition Postulate can significantly boost your problem-solving capabilities in geometry and beyond. UpStudy offers comprehensive support in mathematics as well as other academic subjects! If you require any assistance for any academic discipline, UpStudy is ready to assist!