Question

-
U
TIIULUIl allu answer the following questions.
MD
In figure, AD is a median of a triangle ABC and AM I BC.
BC
4. AD2 + BC .DM +
equals to
5. AD2 - BC. DM +
equals to
2
)
6. 2AD? +
BC equals to​

Answer 1

Answer:

In right angled triangle ABM,

D is the midpoint of BC and AM ⊥ BC.

AB² = AM² + BM² ....(1) - Pythagoras Theorem

In right angled triangle ADM,

AD² = AM² + MD² ....(2) - Pythagoras Theorem

From (1) and (2), we get

AB² = AD² - MD² + BM²

⇒ AB² = AD² - DM² + (BD - DM)²

⇒ AB² = AD² - DM² + BD² + DM² - 2BD × DM

⇒ AB² = AD² - 2BD × DM + BD²

⇒ AB² = AD² - 2(BC/2) × DM + (BC/2)²   {∵ BD = DC = BC/2}

⇒ AB² = AD² - BC × DM + BC²/4

Hence proved.

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Answer 2

Step-by-step explanation:

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