Question 3:

In the following figure, ABC and DBC are two triangles on the same base BC. If AD intersects BC at O, show that 

Answer:

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

In ∆APO and ∆DMO,

∠APO = ∠DMO (Each = 90°)

∠AOP = ∠DOM (Vertically opposite angles)

∴ ∆APO ∼ ∆DMO (By AA similarity criterion)

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