Question

construct $overline{xy}$ congruent to $overline{ab}$.
diagram of segment $\overline{ab}$
intersection $\tilde{y}$ (or x).
d. with the same compass setting, put the compass point on the endpoint of the construction in the first and draw an arc that intersects the ray. label the intersection x or y depending on the name of the ot endpoint.
what does the final construction look like? choose the correct answer below.
\bigcirc a. diagram: $a$ connected to $b$ and $y$ on a ray
\bigcirc b. diagram: $x$---$y$ and $a$---$b$ with an arc at $b$
\bigcirc c. diagram: $a$---$b$ and $x$---$y$ with an arc at $y$
\bigcirc d. diagram: $a$ connected to $y$ and $b$ on a ray

Explanation:

To construct \(\overline{XY}\) congruent to \(\overline{AB}\), we need to ensure that the length of \(\overline{XY}\) is equal to \(\overline{AB}\). Let's analyze each option:

• Option A: There is an extra segment from \(A\) to \(Y\), which is not part of the construction of a congruent segment. The goal is just to have \(\overline{XY}\) with the same length as \(\overline{AB}\), not additional connections.
• Option B: The segment \(\overline{XY}\) is drawn, and the arc at \(B\) (used to measure the length of \(\overline{AB}\)) is also present. The length of \(\overline{XY}\) should match \(\overline{AB}\) since we use the same compass setting (which measures the length of \(\overline{AB}\)) to draw the arc for \(Y\) (or \(X\)). This fits the construction of a congruent segment.
• Option C: There is no arc shown at \(B\) or related to the construction of \(\overline{XY}\) to ensure congruence. We need the arc to transfer the length from \(\overline{AB}\) to \(\overline{XY}\), so this is incorrect.
• Option D: The segment from \(A\) to \(Y\) is incorrect, and the placement of \(B\) and \(Y\) does not align with the construction of a congruent segment \(\overline{XY}\) to \(\overline{AB}\).

Answer:

B. \(\boldsymbol{X}\) ---- \(\boldsymbol{Y}\) (with \(\boldsymbol{A}\) ---- \(\boldsymbol{B}\) and an arc at \(B\) as in the diagram)