Question

ncert maths solutions class 9 chapter 9 exercise 9.3​

Answer 1

Exercise 9.3

Question 1:

In the given figure, E is any point on median AD of a ΔABC. Show that

ar (ABE) = ar (ACE)

Answer:

AD is the median of ΔABC. Therefore, it will divide ΔABC into two triangles of equal

areas.

∴ Area (ΔABD) = Area (ΔACD) … (1)

ED is the median of ΔEBC.

∴ Area (ΔEBD) = Area (ΔECD) … (2)

On subtracting equation (2) from equation (1), we obtain

Area (ΔABD) − Area (EBD) = Area (ΔACD) − Area (ΔECD)

Area (ΔABE) = Area (ΔACE)

Question 2:

In a triangle ABC, E is the mid-point of median AD. Show that ar (BED) = ar (ABC)

AD is the median of ΔABC. Therefore, it will divide ΔABC into two triangles of equal

areas.

∴ Area (ΔABD) = Area (ΔACD)

… (1)

In ΔABD, E is the mid-point of AD. Therefore, BE is the median.

∴ Area (ΔBED) = Area (ΔABE)

Area (ΔBED) = Area (ΔABD)

Area (ΔBED) = Area (ΔABC) [From equation (1)]

Area (ΔBED) = Area (ΔABc

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