Question

vocabulary and core concept check

1. writing explain how $overline{xy}$ and $xy$ are different.
2. different words, same question which is different? find “both” answer

monitoring progress and modeling with mathematics
in exercises 3 - 6, use a ruler to measure the length of the segment to the nearest tenth of a centimeter. (see example 1.)
3.
4.
5.
6.
construction in exercises 7 and 8, use a compass and straightedge to construct a copy of the segment.

1. copy the segment in exercise 3.
2. copy the segment in exercise 4.

Explanation:

Step1: Analyze the symbols in question 1

$\overline{XY}$ represents a line - segment with endpoints $X$ and $Y$. It is a definite part of a line. $XY$ can represent the length of the line - segment $\overline{XY}$. One is a geometric object, the other is a numerical value representing its length.

Step2: Analyze question 2

Given $AC = 3$ and $CB=7$.
For "Find $AC + CB$":
$AC + CB=3 + 7=10$.
For "Find $AB$": By the segment - addition postulate, if $C$ is between $A$ and $B$, then $AB=AC + CB = 10$.
For "Find $CA+BC$": Since addition is commutative, $CA + BC=AC + CB = 10$.
For "Find $BC - AC$": $BC - AC=7 - 3 = 4$.
The different one is "Find $BC - AC$" as its result is different from the others.

Answer:

1. $\overline{XY}$ is a line - segment (a geometric object), while $XY$ is the length of the line - segment $\overline{XY}$ (a numerical value).
2. The different one is "Find $BC - AC$".