Question

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Answer 1

Answer:

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Answer 2

Answer:

For this we can use Pythagoras theorem to prove two right angled triangles ∆ABM and ∆ABC.

Step-by-step explanation:

Proof:

Given,

M is the mid-point of BC

BM=CM=½BC

Since ∆ ABM is Right Angled Triangle

By Pythagoras theorem,

AM²=BM²+AB²

AB²=AM²-BM² ------------ (1)

Also, ∆ ABC is Right Angled Triangle,

By Pythagoras theorem,

AC²=AB²+BC²

AB²=AC²-BC² -------------(2)

From (1) and (2),

L.H.S are equal, R.H.S. also equal.

AM²-BM²=AC²-BC²

AM²+BC²=AC²+BM

Hence Proved