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)
*

Let’s find ∠ P and ∠ R

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°.

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For example
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