Question

1. higher order thinking if points c, d, and e are on a line and cd = 20 and ce = 32, what are the possible values of de?

practice
find the length of each segment. see examples 1 and 2

1. df
2. de
3. fg
4. fh

points a, b, c, d, and e are collinear. see example 3

1. if ac = 16, what is x?
2. what is ab?
3. w

Explanation:

Step1: Analyze position of points

There are two cases for the positions of points C, D, and E on the line.

Case 1: Point D is between C and E

In this case, by the segment - addition postulate, \(CE=CD + DE\). Given \(CD = 20\) and \(CE = 32\), we can solve for \(DE\) by substituting the values into the formula: \(DE=CE - CD\).
\[DE=32 - 20=12\]

Case 2: Point C is between D and E

In this case, \(DE=CD + CE\). Substituting \(CD = 20\) and \(CE = 32\), we get \(DE=20 + 32 = 52\)

Answer:

The possible values of \(DE\) are 12 and 52.