Can a right triangle be isosceles?

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

Now,

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

Now,

  ∠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