Question

"Question 1 In the given figure, E is any point on median AD of a ΔABC. Show that ar (ABE) = ar (ACE)

Class 9 - Math - Areas of Parallelograms and Triangles Page 162"

Answer 1

 The median divides a triangle into two Triangles of equal areas.

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Given:

AD is a median of ∆ABC & E is any point on AD.

To Prove:

ar (ABE) = ar (ACE)

Proof:

Since,AD is median of ΔABC.

 Thus, it will divide ΔABC into two triangles of equal areas.

∴ ar(ABD) = ar(ACD) — (i)

Also,

ED is the median of ΔEBC.

∴ ar(EBD) = ar(ECD) — (ii)

On Subtracting eq (ii) from (i),

ar(ABD) – ar(EBD) = ar(ACD) – ar(ECD)

 ar(ABE) = ar(ACE)

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Hope this will help you...