AM is a median of a triangle ABC. Is AB + BC + CA > 2AM ? (Consider th

1.	AM is a median of a triangle ABC. Is AB + BC + CA > 2AM ? (Consider the sides of triangles Δ ABM and Δ AMC.)
Answer» Since, the sum of lengths of any two sides in a triangle should be greater than the length of third side. Therefore, In ΔABM, AB + BM > AM ……….(i) In ΔAMC, AC + MC > AM ……….(ii) ⇒ AB + AC + (BM + MC) > 2AM ⇒ AB + AC + BC > 2AM Hence, it is true.

AM is a median of a triangle ABC. Is AB + BC + CA > 2AM ? (Consider the sides of triangles Δ ABM and Δ AMC.)

Answer»

Since, the sum of lengths of any two sides in a triangle should be greater than the length of third side.

Therefore,

In ΔABM, AB + BM > AM ……….(i)

In ΔAMC, AC + MC > AM ……….(ii)

⇒ AB + AC + (BM + MC) > 2AM

⇒ AB + AC + BC > 2AM

Hence, it is true.

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AM is a median of a triangle ABC. Is AB + BC + CA &gt; 2AM ? (Consider the sides of triangles Δ ABM and Δ AMC.)

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AM is a median of a triangle ABC. Is AB + BC + CA > 2AM ? (Consider the sides of triangles Δ ABM and Δ AMC.)