मराठी

In the Given Figure, Ad // Be // Cf. Prove that Area (δAec) = Area (δDbf) - Mathematics

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प्रश्न

In the given figure, AD // BE // CF.
Prove that area (ΔAEC) = area (ΔDBF)

बेरीज
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उत्तर

We know that the area of triangles on the same base and between the same parallel lines are equal.

Consider ABED quadrilateral; AD || BE.
With the common base, BE and between AD and BE parallel lines, we have
Area of ΔABE = Area of ΔBDE

Similarly, in BEFC quadrilateral, BE || CF
With common base BC and between BE and CF parallel lines, we have
Area of ΔBEC = Area of ΔBEF

Adding both equations, we have
Area of ΔABE + Area of ΔBEC = Area of ΔBEF + Area of ΔBDE
⇒ Area of AEC = Area of DBF

Hence Proved.

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Figures Between the Same Parallels
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 16: Area Theorems [Proof and Use] - Exercise 16 (A) [पृष्ठ १९७]

APPEARS IN

सेलिना Concise Mathematics [English] Class 9 ICSE
पाठ 16 Area Theorems [Proof and Use]
Exercise 16 (A) | Q 16 | पृष्ठ १९७

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