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Chapter 5: Q19 (page 181)

Given: 鈻�ABCD; BE炉鈭�MD炉;

M is the midpoint of AB炉;

Prove: DE=BC

Short Answer

Expert verified

It is proved DE炉=BC炉.

Step by step solution

01

Step 1. Consider the diagram.

Here ABCD is a parallelogram, BE炉鈭�MD炉and M is the midpoint of AB炉.

02

Step 2. Show the prove.

In 螖ABE, MD炉鈭�BE炉 and M is the midpoint of AB炉.

So,

D is a midpoint of AE炉.

(According to the converse of midpoint theorem, if a line is drawn through the midpoint of a side of a triangle parallel to the other side, then it bisects the third side.)

As D is a midpoint of AE炉,

AD炉=DE炉 鈥︹�� (i)

Now,

ABCD is a parallelogram.

So,

AD炉=BC炉 鈥︹�� (ii) (Opposite sides of a parallelogram are equal.)

From (i) and (ii),

DE炉=BC炉

03

Step 3. State the conclusion.

Therefore, DE炉=BC炉(proved).

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Most popular questions from this chapter

Give the reason for each step in the following proof of theorem 5-6

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Proof:

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Draw and label a diagram. List what is given and what is to be proved. Then write a two-column proof of the theorem.

Theorem 5-4.
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