CBSE Class 9 Answered
XY is a line parallel to the side BC of a ABC. BE AC and CF AB meets XY at E and F respectively. Show that ar (ABE) = ar (ACF).
Asked by Topperlearning User | 04 Jun, 2014, 01:23: PM
Expert Answer
Given: ABC, such that BE AC and CF AB
Proof: since YE BC and BE CY
BCYE is a parallelogram.
Similarly, BCFX is a parallelogram.
Parallelograms BCFX and BCYE are on the same base BC and between same parallels BC and EF,
ar (BCYE) = ar (BCFX) …(i)
ar (ABE) = ar (BCYE) …(ii) ( on same base and between same parallels)
Similarly ar (ACF) = ar (BCFX) …(iii)
From (i), (ii) and (iii)
Hence ar (ABE) = ar (ACF)
Answered by | 04 Jun, 2014, 03:23: PM
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