Question

omar is asked to construct $overline{xy}$ which is congruent to $overline{ab}$. he constructed figures shown below: in figure (i) he marked point $y$ by drawing an arc of radius 3 inches and taking point $x$ as the center. in figure (ii) he marked point $x$ by drawing an arc of radius 3 inches and taking point $y$ as the center. which statement is true? only figure (i) is congruent to $overline{ab}$. only figure (ii) is congruent to $overline{ab}$. both figure (i) and figure (ii) are congruent to $overline{ab}$. neither figure (i) nor figure (ii) is congruent to $overline{ab}$.

Explanation:

Step1: Recall congruent - segment concept

Two line - segments are congruent if they have the same length. Segment $\overline{AB}$ has a length of 3 inches.

Step2: Analyze Figure (i)

In Figure (i), an arc of radius 3 inches is drawn with point $X$ as the center to mark point $Y$. So, the length of $\overline{XY}$ is 3 inches, which is the same as the length of $\overline{AB}$.

Step3: Analyze Figure (ii)

In Figure (ii), an arc of radius 3 inches is drawn with point $Y$ as the center to mark point $X$. So, the length of $\overline{XY}$ is 3 inches, which is the same as the length of $\overline{AB}$.

Answer:

Both Figure (i) and Figure (ii) are congruent to $\overline{AB}$.