Question

1.2 exercise
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” answers.

find $ac + cb$
find $bc - ac$
find $ab$
find $ca+bc$

Explanation:

1. $\overline{XY}$ represents a line - segment with endpoints $X$ and $Y$. It has a definite length. $XY$ can represent the length of the line - segment $\overline{XY}$. So, one is a geometric object (the line - segment) and the other is a numerical value (the length of the line - segment).
2. By the segment - addition postulate, if $C$ is a point on $\overline{AB}$, then $AC + CB=AB$ and $CA + BC = AB$. So, the expressions "Find $AC + CB$", "Find $AB$", and "Find $CA+BC$" are equivalent. The different one is "Find $BC - AC$" as it does not equal the length of $\overline{AB}$ like the others.

Answer:

1. $\overline{XY}$ is a line - segment, $XY$ is its length.
2. The different one is "Find $BC - AC$".