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In triangleAbc, D and E Are the Mid-points of Ab and Ac Respectively. Find the Ratio of the Areas of δAde and δAbc - Mathematics

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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

 RD Sharma Solution for Class 10 Maths (2018 (Latest))
Chapter 7: Triangles
Ex. 7.6 | Q: 9 | Page no. 95
 RD Sharma Solution for Class 10 Maths (2018 (Latest))
Chapter 7: Triangles
Ex. 7.6 | Q: 9 | Page no. 95

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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.
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