If D- E are the mid-points of AB- AC of ABC and DE - BC then - -

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Standard IX

Mathematics

Two Triangles Having the Same Base & Equal Areas

If D, E are...

Question

If $D, E$ are the mid-points of $A B$ , $A C$ of $△ A B C$ and $¯ ¯¯¯¯¯¯¯ ¯ D E = λ ¯ ¯¯¯¯¯¯ ¯ B C$ then $λ$ =

1

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2

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\frac{1}{2}

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3

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Solution

The correct option is C $\frac{1}{2}$
By mid point theorem, if $D$ and $E$ are mid points of $A B$ and $A C$ , then
$¯ D E = \frac{1}{2} ¯ B C$ ------ $(1)$
As per question $¯ D E = λ ¯ B C$ -------- $(2)$
From $(1)$ and $(2)$ , comparing, we get
$λ = 1 / 2$
So, option $(C)$ is correct.

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If D,E are the mid-points of AB, AC of △ABC and ¯¯¯¯¯¯¯¯¯DE=λ¯¯¯¯¯¯¯¯BC then λ =

The correct option is C 12By mid point theorem, if D and E are mid points of AB and AC, then ¯DE=12¯BC ------ (1)As per question ¯DE=λ¯BC -------- (2)From (1) and (2), comparing, we get λ=1/2So, option (C) is correct.

If $D, E$ are the mid-points of $A B$ , $A C$ of $△ A B C$ and $¯ ¯¯¯¯¯¯¯ ¯ D E = λ ¯ ¯¯¯¯¯¯ ¯ B C$ then $λ$ =

The correct option is C $\frac{1}{2}$
By mid point theorem, if $D$ and $E$ are mid points of $A B$ and $A C$ , then
$¯ D E = \frac{1}{2} ¯ B C$ ------ $(1)$
As per question $¯ D E = λ ¯ B C$ -------- $(2)$
From $(1)$ and $(2)$ , comparing, we get
$λ = 1 / 2$
So, option $(C)$ is correct.