In the given figure- D and E are mid points of sides AB and AC of ABC- Which of the following is correct-A- DE -1-2 BC- by mid point theoremB- DE - I -2 BC- by converse of mid point theoremC- DE - I -2 AB- by mid point theoremD- DE - I -2 AB- by converse of mid point theorem

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Midpoint Theorem

In the given ...

Question

In the given figure, $D$ and $E$ are mid points of sides $A B$ and $A C$ of $△ A B C .$ Which of the following is correct?

$D E = \frac{1}{2} B C,$ by mid point theorem

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$D E = \frac{1}{2} B C,$ by converse of mid point theorem

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$D E = \frac{1}{2} A B,$ by mid point theorem

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$D E = \frac{1}{2} A B,$ by converse of mid point theorem

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Solution

The correct option is A
$D E = \frac{1}{2} B C,$ by mid point theorem

Mid point theorem states that a line joining the mid points of two sides of a triangle is parallel to the third side and is half of it.

Therefore, by mid point theorem, $D E = \frac{1}{2} B C$ and $D E ∥ B C$

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Similar questions

Q. In the given figure, D and E are mid points of sides AB and AC respectively of

Δ

ABC. Which of the following is true ?

Q. Prove the converse of the mid-point theorem following the guidelines given below: Consider a triangle

A B C

with

D

as the mid-point of

A B

. Draw

D E ∥ B C

to intersect

A C

E

. Let

E_{1}

be the mid-point of

A C

. Use mid-point theorem to get

D E_{1} ∥ B C

and

D E_{1} = B C / 2

. Conclude

E = E_{1}

and hence

E

is the mid-point of

A C

△

ABC, D is mid-point of AB, and E is mid-point of BC. Calculate :

D E

, if

A C = 6.4

cm,

In the given figure, if D and E are the mid points of sides AB and AC, respectively, and DE is produced to F such that E is the mid point of FD, which of the following options is correct?

Q. If

D, E

are the mid-points of

A B

A C

△ A B C

and

¯ ¯¯¯¯¯¯¯ ¯ D E = λ ¯ ¯¯¯¯¯¯ ¯ B C

then

λ

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In the given figure, D and E are mid points of sides AB and AC of △ABC. Which of the following is correct?

The correct option is A DE=12BC, by mid point theorem Mid point theorem states that a line joining the mid points of two sides of a triangle is parallel to the third side and is half of it. Therefore, by mid point theorem, DE=12BC and DE∥BC

In the given figure, $D$ and $E$ are mid points of sides $A B$ and $A C$ of $△ A B C .$ Which of the following is correct?

The correct option is A
$D E = \frac{1}{2} B C,$ by mid point theorem

Mid point theorem states that a line joining the mid points of two sides of a triangle is parallel to the third side and is half of it.

Therefore, by mid point theorem, $D E = \frac{1}{2} B C$ and $D E ∥ B C$