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?

Explanation:

Step1: Consider two - point order cases

There are two possible arrangements of points C, D, and E on the line.

Step2: Case 1: 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 $DE$ as $DE=CE - CD$. Substituting the values, we get $DE=32 - 20=12$.

Step3: Case 2: 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.