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Prove that in a triangle other …

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Prove that in a triangle other than an equilateral triangle , angle opposite to the longest side is greater than 2/3 of right angle
  • 1 answers

Yogita Ingle 3 years, 8 months ago

Given -- ΔABC other than equilateral triangle.

The construction is already given in the picture.So let me just establish the relation between the sides.
Let  AB = AD = DB

ABD is an equilateral triangle since AB = AD = DB

∠ABD = ∠ADB = ∠BAD = 60°

Longest side= BC
Angle opposite to longest side = ∠BAC

Here it is clear that ∠BAC = ∠BAD + ∠CAD
So ∠BAC > ∠BAD
∠BAC > 60°

2/3 of right angle = 2/3 × 90 = 60

SO,
angle(BAC) > 2/3 of right angle

 

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