Question

In triangle ABC, E is the midpoint of median AD. Show that ar(triangle BED) =1/4 ar(triangle ABC) ​

Answer 1

Step-by-step explanation:

Given;

AD is a median.

E is the midpoint of median AD.

To prove : ar(∆ BED) =1/4 ar(∆ ABC)

Proof: We know that median falls on the midpoint of the side of a triangle, thus dividing it in two triangle with equal areas.

Hence, keeping this fact in our mind, it can be concluded;

ar(∆ADB) = ar( ∆ADC)

or, ar(∆ADB) = 1 /2 ar(∆ABC) (i)

Now, BE is falling on the midpoint of AD. Thus we can say that BE is a median for ∆ADB since its falling the midpoint of side AD of ∆ADB.

Hence, ar(∆BED) = ar(∆BEA)

Therefore, ar(∆BED) = 1/2 ar(∆ADB)

ar(∆BED) = 1/2 {1 /2 ar(∆ABC)} (from eq. i)

ar(∆BED) = 1/4 ar(∆ABC);

Thus, ar(∆BED) = 1/4 ar(∆ABC);

That's all.

Answer 2

Answer:

Step-by-step explanation:

hey here is your proof in above pics

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