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Theorem 9.3 : Two triangles having the s...

Theorem 9.3 : Two triangles having the same base (or equal bases) and equal areas lie between the same parallels.

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Since `CEbotAB` and `DFbotAB` Since, lines are perpendicular to same line are parallel to each other.
`CE||DF`
Now,
`ar(ABC)=1/2xxbb"Base"xxBB'Height"`
`ar(ABC)=1/2xxABxxCE`
Similarly, ...
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Knowledge Check

  • If P,R,T are the area of a parallelogram , a rhombus and a triangle standing on the same base and between the same parallels, which of the following is true ?

    A
    `R le P le T`
    B
    `PgtRgtT`
    C
    R=P=T
    D
    R=P=2T

  • Two parallelograms are on equal bases and between the same parallels. The ratio of their areas is

    A
    `1 : 2`
    B
    `1 : 1`
    C
    `2 : 1`
    D
    `3 : 1`

  • Which of the following figures lie on the same base and between the same parallels ?

    A
    B
    C
    D
    all of these

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    Triangles on the same base and between the same parallels are equal in area. GIVEN : Two triangles A B C and P B C on the same base B C and between the same parallel lines B C and A Pdot TO PROVE : a r( A B C)=a r( P B C) CONSTRUCTION : Through B , draw B D C A intersecting P A produced in D and through C , draw C Q B P , intersecting line A P in Q.

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