CBSE Class 10CBSE
Share
Notifications

View all notifications
Books Shortlist
Your shortlist is empty

Solution for In Figure, ABC and DBC are two triangles on the same base BC. If AD intersects BC at O, show that (ar(ABC))/(ar(DBC)) = (AO)/(DO) - CBSE Class 10 - Mathematics

Login
Create free account


      Forgot password?

Question

In Figure, ABC and DBC are two triangles on the same base BC. If AD intersects BC at O, show that `(ar(ABC))/(ar(DBC)) = (AO)/(DO)`

Solution

Let us draw two perpendiculars AP and DM on line BC.

We know that area of a triangle = 1/2 x Base x Height

`:.(ar(triangleABC))/(ar(triangleDBC)) =  (1/2 BC XX AP)/(1/2BCxxDM)) = (AP)/(DM)`

In ΔAPO and ΔDMO,

∠APO = ∠DMO (Each = 90°)

∠AOP = ∠DOM (Vertically opposite angles)

∴ ΔAPO ∼ ΔDMO (By AA similarity criterion)

`:. (AP)/(DM) = (AO)/(DO)`

`=> (ar(triangleABC))/(ar(triangleDBC))=(AO)/(DO)`

  Is there an error in this question or solution?

APPEARS IN

Video TutorialsVIEW ALL [1]

Solution In Figure, ABC and DBC are two triangles on the same base BC. If AD intersects BC at O, show that (ar(ABC))/(ar(DBC)) = (AO)/(DO) Concept: Areas of Similar Triangles.
S
View in app×