In the given figure- AD - BE - CF- Prove that - area - AEC - area - DBF- State 1 if true or 0 false

In the given figure, #160;AD ∥ BE ∥ CF .Since, #160; #160;AD ∥ BE Area ( ABE) = Area ( DEB) #160; #160;[The area of triangles on the same ( ...

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Standard IX

Mathematics

Area of a Triangle

In the given ...

Question

In the given figure, AD || BE || CF. Prove that : area ( $Δ A E C$ ) = area ( $Δ D B F$ ). State 1 if true or 0 false

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Solution

In the given figure, $A D ∥ B E ∥ C F$ .

Since, $A D ∥ B E$

$A r e a (△ A B E) = A r e a (△ D E B)$ [The area of triangles on the same (or equal) base and between the same two parallels are equal.] ....(1)

Since, $B E ∥ C F$

$A r e a (△ B E C) = A r e a (△ B F E)$ [The area of triangles on the same (or equal) base and between the same two parallels are equal.] ......(2)

Add equation (1) and (2),

$A r e a (△ A B E) + A r e a (△ B E C) = A r e a (△ D E B) + A r e a (△ B F E)$

$A r e a (△ A E C) = A r e a (△ D B F)$

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In the given figure, AD || BE || CF. Prove that : area (ΔAEC) = area (ΔDBF). State 1 if true or 0 false

In the given figure, AD || BE || CF. Prove that : area ( $Δ A E C$ ) = area ( $Δ D B F$ ). State 1 if true or 0 false