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# Solution - In the given figure, ABCDE is a pentagon. A line through B parallel to AC meets DC produced at F. Show that - CBSE Class 9 - Mathematics

ConceptTriangles on the Same Base and Between the Same Parallels

#### Question

In the given figure, ABCDE is a pentagon. A line through B parallel to AC meets DC produced at F. Show that

(i) ar (ACB) = ar (ACF)

(ii) ar (AEDF) = ar (ABCDE)

#### Solution

(i) ΔACB and ΔACF lie on the same base AC and are between

The same parallels AC and BF.

∴ Area (ΔACB) = Area (ΔACF)

(ii) It can be observed that

Area (ΔACB) = Area (ΔACF)

⇒ Area (ΔACB) + Area (ACDE) = Area (ACF) + Area (ACDE)

⇒ Area (ABCDE) = Area (AEDF)

Is there an error in this question or solution?

#### APPEARS IN

NCERT Mathematics Textbook for Class 9 (with solutions)
Chapter 9: Areas of Parallelograms and Triangles
Q: 11 | Page no. 163

#### Reference Material

Solution for question: In the given figure, ABCDE is a pentagon. A line through B parallel to AC meets DC produced at F. Show that concept: Triangles on the Same Base and Between the Same Parallels. For the course CBSE
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