Question

In exercises 26-29, complete each statement about the diagram. Then state the definition, postulate or theorem that justifies your answer.

If$\mathbf{MP}\mathbf{=}\mathbf{PO}$ and $\overline{\mathrm{PQ}}\parallel \overline{\mathrm{ON}}$, then Q is the$\underset{\_}{?}$ of$\underset{\_}{?}$ .

Short answer

If$MP=PO$ and $\overline{PQ}\parallel \overline{ON}$, then Q is the midpointof$\mathbf{MN}$ .

The theorem that justifies the answer is the theorem 5-10 which states thata line that contains the midpoint of one side of a triangle and is parallel to another side passes through the midpoint of the third side.

Step-by-step solution

- Observe the given diagram.

The given diagram is:

- Write the theorem 5-10

The theorem 5-10 states that a line that contains the midpoint of one side of a triangle and is parallel to another side passes through the midpoint of the third side.

- Description of step.

As$MP=PO$ , therefore P is the midpoint of $MO$.

Therefore, the line thatcontains the midpoint of one side of a triangle and is parallel to another side passes through the midpoint of the third side.

Therefore$\overline{PQ}\parallel \overline{ON}$, and Q is the midpoint of third side.

If$MP=PO$ and$\overline{PQ}\parallel \overline{ON}$ , then Q is the midpointof$\mathbf{MN}$ .

The theorem that justifies the answer is the theorem 5-10 which states that a line that contains the midpoint of one side of a triangle and is parallel to another side passes through the midpoint of the third side.