Question

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

If$\mathbf{LM}\mathbf{=}\mathbf{ON}$ and $\mathbf{LO}\mathbf{=}\mathbf{MN}$, then$\mathbf{LMNO}$ is a$\underset{\_}{?}$ .

Short answer

If$LM=ON$ and $LO=MN$, then$LMNO$ is a parallelogram.

The theorem that justifies the answer is the theorem 5-4 which states thatif both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

Step-by-step solution

- Observe the given diagram.

The given diagram is:

- Write the theorem 5-4.

The theorem 5-4 states that if both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

- Description of step.

It is being given that$LM=ON$ and$LO=MN$ .

Therefore, it has been given that the opposite sides of the quadrilateral$LMNO$ are congreunt, thereore the quadrilateral$LMNO$ is a parallelogram.

Therefore, If$LM=ON$ and$LO=MN$ , then$LMNO$ is a parallelogram.

The theorem that justifies the answer is the theorem 5-4 which states that if both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.