Share
Notifications

View all notifications

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) - 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

 NCERT Solution for Mathematics Textbook for Class 10 (2019 (Latest))
Chapter 6: Triangles
Ex. 6.4 | Q: 3 | Page no. 144
 RD Sharma Solution for Class 10 Maths (2018 (Latest))
Chapter 7: Triangles
Ex. 7.6 | Q: 19 | Page no. 96
 RD Sharma Solution for Class 10 Maths (2018 (Latest))
Chapter 7: Triangles
Ex. 7.6 | Q: 19 | Page no. 96

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×