Chapter 5: Q19 (page 181)

Given: $▱ ABCD$ ; $\bar{BE} ∥ \bar{MD}$ ;
M is the midpoint of $\bar{AB}$ ;
Prove: $DE = BC$

Short Answer

Expert verified

It is proved $\bar{D E} = \bar{B C}$ .

Step by step solution

Step 1. Consider the diagram.

Here ABCD is a parallelogram, $\bar{B E} ∥ \bar{M D}$ and M is the midpoint of $\bar{A B}$ .

Step 2. Show the prove.

In $Δ A B E$ , $\bar{M D} ∥ \bar{B E}$ and M is the midpoint of $\bar{A B}$ .

So,

D is a midpoint of $\bar{A E}$ .

(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 $\bar{A E}$ ,

$\bar{A D} = \bar{D E}$ …… (i)

Now,

ABCD is a parallelogram.

So,

$\bar{A D} = \bar{B C}$ …… (ii) (Opposite sides of a parallelogram are equal.)

From (i) and (ii),

$\bar{D E} = \bar{B C}$

Step 3. State the conclusion.

Therefore, $\bar{D E} = \bar{B C}$ (proved).

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Given: $▱ ABCD$ ; $\bar{BE} ∥ \bar{MD}$ ;
M is the midpoint of $\bar{AB}$ ;
Prove: $DE = BC$

Short Answer

Step by step solution

Step 1. Consider the diagram.

Step 2. Show the prove.

Step 3. State the conclusion.

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Given: ▱ABCD; BE¯∥MD¯; M is the midpoint of AB¯;Prove: DE=BC

Short Answer

Step by step solution

Step 1. Consider the diagram.

Step 2. Show the prove.

Step 3. State the conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Statistics

Discrete Mathematics

Applied Mathematics

Calculus

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Given: $▱ ABCD$ ; $\bar{BE} ∥ \bar{MD}$ ;
M is the midpoint of $\bar{AB}$ ;
Prove: $DE = BC$