In the given figure- D and E are mid points of sides AB and AC respectively of - ABC- Which of the following is true -A- DE - BC -2- by mid point theoremB- DE - B 2 C -2- by converse of mid point theoremC- DE - AB -2- by mid point theoremD- DE - AB -2- 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 AB and AC respectively of $Δ$ ABC. Which of the following is true ?

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

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

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

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

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Solution

The correct option is A $D E = \frac{B C}{2}, by mid point theorem$
Mid point theorem states that a line joining the mid- points of 2 sides of a triangle is parallel to the third side and is half of it.
Therefore, by mid point theorem, $D E = \frac{B C}{2}$ and $D E | | B C$ .

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Similar questions

In the given figure, D and E are mid points of sides AB and AC of $△$ 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,

Q. In a ∆ABC, D and E are the mid-points of AB and AC respectively and DE = 5.6 cm. Find the length of BC.

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?

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In the given figure, D and E are mid points of sides AB and AC respectively of ΔABC. Which of the following is true ?

The correct option is A DE=BC2,by mid point theoremMid point theorem states that a line joining the mid- points of 2 sides of a triangle is parallel to the third side and is half of it. Therefore, by mid point theorem, DE=BC2 and DE || BC.

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 ?

The correct option is A $D E = \frac{B C}{2}, by mid point theorem$
Mid point theorem states that a line joining the mid- points of 2 sides of a triangle is parallel to the third side and is half of it.
Therefore, by mid point theorem, $D E = \frac{B C}{2}$ and $D E | | B C$ .