Q31. - Geometry

Question

In the following figure, $\overline{PR}\cong \overline{RT}, S$ is the midpoint of $\overline{RT}, QR=4, ST=5$. Complete the following statements:

a. $RS=\_\_$

b. $RT=\_\_$

c. $PR=\_\_$

d. $PQ=\_\_$

Step-by-Step Solution

Answer

a. $RS=5$

b. $RT=10$

c. $PR=10$

d. $PQ=6$

Part a. Step 1. Check the figure.

Consider the figure.

Part a. Step 2. Step description.

From the figure, the point $S$ is the midpoint of $RT$.

 

So, the distance between $RT$ and $RS$ must be the same.

Part a. Step 3. Step description.

Since the distance between $RT$ and $RS$ must be the same, thus $RS=5$.

 

Therefore, $RS=5$.

Part b. Step 1. Check the figure.

Consider the figure.

Part b. Step 2. Step description.

From the figure, the point $S$ is the midpoint of $RT$.

 

So, the distance between $RT$ and $RS$ must be the same.

Part b. Step 3. Step description.

Since the distance between $RT$ and $RS$ must be the same, thus find the distance as follows:

$$\begin{gathered} RT=RS+ST \\ =5+5 \\ =10 \end{gathered}$$

 

Therefore, $RT=10$.

Part c. Step 1. Check the figure.

Consider the figure.

Part c. Step 2. Step description.

From the figure, the line $PR\cong RT$.

 

So, the distance between $RT$ and $PR$ must be the same.

Part c. Step 3. Step description.

Since the distance between $RT$ and $PR$ must be the same, thus $PR=10$.

 

Therefore, $PR=10$.

Part d. Step 1. Check the figure.

Consider the figure.

Part d. Step 2. Step description.

From the figure, the line $PR\cong RT$.

 

So, the distance between $RT$ and $PR$ must be the same.

Part d. Step 3. Step description.

Since the distance between $RT$ and $PR$ must be the same, thus find the distance as follows:

$$\begin{gathered} PQ=PR-QR \\ =10-4 \\ =6 \end{gathered}$$

 

Therefore, $PQ=6$.