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Chapter 5: Q21 (page 181)

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

Short Answer

Expert verified

MP=12EF

Step by step solution

01

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:

02

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,

PM鈭�EF

Hence,

PM=12EF

03

Step 3. State the conclusion.

Therefore, PM=12EF(proved).

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