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Show that a median of a triangle divide...

Show that a median of a triangle divides it into two triangles of equal areas.

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Please refer to the diagram in the video.
Here, `AD` is median to `BC` such that `BD=CD`
and `AE_|_BC`. `ar(ABD) = 1/2xxAExxBD`
`=1/2xxAExxCD`(as BD=CD)
`=ar(ACD)`
As, `ar(ABD) = ar(ACD)`,
it shows a median of a triangle divides it into two triangles of equal areas.
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Knowledge Check

  • The median of a triangle divides it into two

    A
    triangles of equal area
    B
    congruent triangles
    C
    right angled triangles
    D
    isosceles triangles

  • Assertion (A) : If ABCD is a rhombus whose one angle is 60^(@) then the ratio of the lengths of its diagonals is sqrt3 : 1 Reason (R ) : Median of a triangle divides it into two triangle of equal area.

    A
    Both Assertion (A) and Reason (R ) are true and Reason (R ) is a correct explansion of Assertion (A).
    B
    Both Assertion (A) and Reason (R ) are true but Reason (R ) is not a correct explansion of Assertion (A).
    C
    Assertion (A) is true and Reason (R ) is false.
    D
    Assertion (A) is false and Reason (R ) is true.

  • Consider the following statements in respect of any triangle I. The three medians of a triangle divide it into six triangles of equal area. II. The perimeter of a triangle is greater than the sum of the lengths of its three medians. Which of the statements given above is/are correct ?

    A
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    C
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    D
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