Chapter 5: Q21 (page 181)

EFGH is a parallelogram whose diagonals intersect at P. M is the midpoint of $\bar{FG}$ . Prove that $MP = \frac{1}{2} EF$ .

Short Answer

Expert verified

$MP = \frac{1}{2} EF$

Step by step solution

Step 1. Consider the diagram.

EFGH is a parallelogram whose diagonals intersect at P. M is the midpoint of FG.

Join the line MP as shown below:

Step 2. Show the calculation.

From the diagram,

P is the diagonal of the parallelogram EFGH.

Hence, diagonals of a parallelogram bisect each other.

Thus, P is the midpoint of side EG. M is the midpoint of side FG.

According to the midpoint theorem,

$P M ∥ E F$

Hence,

$P M = \frac{1}{2} E F$

Step 3. State the conclusion.

Therefore, $P M = \frac{1}{2} E F$ (proved).

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EFGH is a parallelogram whose diagonals intersect at P. M is the midpoint of $\bar{FG}$ . Prove that $MP = \frac{1}{2} EF$ .

Short Answer

Step by step solution

Step 1. Consider the diagram.

Step 2. Show the calculation.

Step 3. State the conclusion.

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EFGH is a parallelogram whose diagonals intersect at P. M is the midpoint of FG¯. Prove that MP=12EF.

Short Answer

Step by step solution

Step 1. Consider the diagram.

Step 2. Show the calculation.

Step 3. State the conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

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EFGH is a parallelogram whose diagonals intersect at P. M is the midpoint of $\bar{FG}$ . Prove that $MP = \frac{1}{2} EF$ .