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Triangles

Question 5:

In the given figure, AD is a median of a triangle ABC and AM ⊥ BC. Prove that:

(i)

(ii)

(iii)

Answer:

(i) Applying Pythagoras theorem in ΔAMD, we obtain

AM2 + MD2 = AD2 … (1)

Applying Pythagoras theorem in ΔAMC, we obtain

AM2 + MC2 = AC2

AM2 + (MD + DC)2 = AC2

(AM2 + MD2) + DC2 + 2MD.DC = AC2

AD2 + DC2 + 2MD.DC = AC2 [Using equation (1)]

Using the result, , we obtain

(ii) …

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