#### Question

In ΔABC, D and E are the mid-points of AB and AC respectively. Find the ratio of the areas of ΔADE and ΔABC

#### Solution

We have, D and E as the mid-points of AB and AC

So, according to the mid-point theorem

DE || BC and DE `=1/2`BC ...(i)

In ΔADE and ΔABC

∠A = ∠A [Common]

∠ADE = ∠B [Corresponding angles]

Then, ΔADE ~ ΔABC [By AA similarity]

By area of similar triangle theorem

`("Area"(triangleADE))/("Area"(triangleABC))="DE"^2/"BC"^2`

`=(1/2BC)^2/"BC"^2` [From (i)]

`=(1/4BC^2)/"BC"^2`

`=1/4`

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#### APPEARS IN

Solution In triangleAbc, D and E Are the Mid-points of Ab and Ac Respectively. Find the Ratio of the Areas of δAde and δAbc Concept: Areas of Similar Triangles.