Q10 - Geometry

Question

For the following figure, name the three segments congruent to $\overline{PQ}$.

Step-by-Step Solution

Answer

The three segments are congruent to $\overline{PQ}$ are $\overline{\mathbf{Q}\mathbf{R}}$, $\overline{\mathbf{R}\mathbf{S}}$, $\overline{\mathbf{S}\mathbf{T}}$.

Step 1. Check the figure.

Consider the figure.

Step 2. Define the concept.

The midpoint of a segment is a point that divides the segment into two congruent segments.

Here from the number line, the segment $\overline{PT}$ is divided into four equal parts. 

Step 3. Step description.

As the segment $\overline{PT}$ is divided into four equal parts $\overline{QR}$, $\overline{RS}$, $\overline{ST}$ and thus these are congruent to the segment $\overline{PT}$.

 

Hence, the segments $\overline{QR}$, $\overline{RS}$, $\overline{ST}$ are congruent to the segment  .