In figure, BD and CE intersect each other at the point P. Is ∆PBC ∼ ∆PDE?

Question

In figure, BD and CE intersect each other at the point P. Is ∆PBC ∼ ∆PDE? Why?

Philoid · Accepted Answer

(True)

In ∆PBC and ∆PDE,

∠BPC = ∠EPD [vertically opposite angles]

Since, ∠BPC of ∆PBC is equal to ∠EPD of ∆PDE and the sides including these.

So,

∆PBC ∼ ∆PDE by SAS similarity criteria.