Q11. - Geometry

Question

Given the diagram, tell whether you can reach the conclusion shown.

If $\overline{AC}$ bisects $\overline{BD}$, name two congruent segments.

Step-by-Step Solution

Answer

The required segments are $\overline{BX}$ and $\overline{DX}$.

Step 1. Observe the given figure.

The midpoint $X$ represents the intersection and bisection of the given lines.

Step 2. Determine the segments that are congruent by using the observation.

As the given lines are also intersecting at the point $X$ and this point represents itself as the midpoint so the segments which are congruent will be $\overline{BX}$ and $\overline{DX}$.

Step 3. Make the conclusion.

The derived segments are $\overline{BX}$ and $\overline{DX}$ so the required segments are $\overline{BX}$ and $\overline{DX}$.