Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • Prove that in a triangle, other than an equilateral triangle, angle opposite the longest side is greater than 2 divided 3 of a right angle

Prove that in a triangle, other than an equilateral triangle, angle opposite the longest side is greater than \frac{2}{3} of a right angle

Answers (1)

Given: ABC is triangle and AC is longest side

To Prove: \angle ABC > \frac{2}{3}\times 90^{\circ}

Proof: AC is longest side

\Rightarrow\angle B > \angleC                                                    (angle opposite to longest side is greaten)

\angleB > \angleA

By adding both

\angleB + \angleB > \angleC + \angleA

2\angleB > \angleC +\angleA

2\angleB + \angleB > \angleC + \angleA + \angleB             (adding \angleB to LHS and RHS)

3\angleB >\angleC + \angleA + \angleB

3\angleB > 180°                                                     (Sum of all interior angles in triangle is 180°)

\angleB > 60°

\Rightarrow \angle B > \frac{2}{3}\times 90^{\circ}

Hence proved.

Posted by

infoexpert24

View full answer

Similar Questions

Latest Question