Chapter 5: Q. 29 (page 201)

In exercises 26-29, complete each statement about the diagram. Then state the definition, postulate or theorem that justifies your answer.
If $\bar{PQ} ∥ \bar{ON}$ , $PR = RO$ and $QS = SN$ then $RS = \frac{1}{2} (\underline{?} + \underline{?})$ .

Short Answer

Expert verified

If $\bar{P Q} ∥ \bar{O N}$ , $P R = R O$ and $Q S = S N$ then $R S = \frac{1}{2} (PQ + ON)$ .

The theorem that justifies the answer is the theorem 5-19 which states thatthe median of the trapezoid is parallel to the bases and has a length equal to the average of the base lengths.

Step by step solution

- Observe the given diagram.

The given diagram is:

- Write the theorem 5-19

The theorem 5-19 states that the median of the trapezoid is parallel to the bases and has a length equal to the average of the base lengths.

- Description of step.

As, $\bar{P Q} ∥ \bar{O N}$ , therefore $P Q N O$ is a trapezoid.

As, $P R = R O$ and $Q S = S N$ therefore, $R S$ is the median of the trapezoid $P Q N O$ .

Therefore, length of the median $R S$ is the average of the base lengths $P Q$ and $N O$ .

If $\bar{P Q} ∥ \bar{O N}$ , $P R = R O$ and $Q S = S N$ then $R S = \frac{1}{2} (PQ + ON)$ .

The theorem that justifies the answer is the theorem 5-19 which states that the median of the trapezoid is parallel to the bases and has a length equal to the average of the base lengths.