Question

D is any point on side AC of triangle ABC with AB = AC. Show that CD<BD.

Answer 1

Since, AB = AC, angABC = angACB. - 1) Now, angABC = angABD + angDBC       => angDBC = angABC - angABD       => angDBC < angABC       => angDBC < ang ACB {using 1))}       => DC < BD  ( side corresponding to larger angle is larger than side corresponding to smaller angle)

Answer 2

Since, AB = AC, angABC = angACB. - 1)

Now, angABC = angABD + angDBC       => angDBC = angABC - angABD       => angDBC < angABC       => angDBC < ang ACB {using 1))}       => DC < BD  ( side corresponding to larger angle is larger than side corresponding to smaller angle)

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