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In a right angled triangle , one angle is of 90°

and In isosceles triangle two sides are equal


Let us consider a right triangle ΔPQR




For a right angled triangle PQR to be isosceles


We make two sides of a right triangle equal


Since PR is hypotenuse i.e. the longest side

Hence, it can’t be equal to any other side

Thus, other two sides are equal

∴ PQ = PR

Can a right triangle be isosceles? - Part 2



  ∠P = ∠R                 (Angles opposite to equal sides of a triangle are equal)


In ∆PQR, right angled at Q.

By angle Sum property,

  ∠P + ∠Q + ∠R = 180°

  ∠R + 90° + ∠R = 180°       

  2∠R = 180° − 90°

          2∠R = 90°

  ∠R = (90°)/2

  ∠R =  45°


∴ ∠P = ∠R = 45°


Let’s find ∠ P and ∠ R


So, every right angled isosceles triangle has an angle of 90° and two angle of 45°.

For example

Can a right triangle be isosceles? - Part 3

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.