Hello Jitendra
Let's remember the properties of parallelograms
- Opposite angles equal
- Opposite sides equal
And
Rectangle has
- Opposite sides equal
- All angles 90
Now,
Parallelogram with one angle 90 means
Assume angle A = 90. So,
- Opposite sides are equal
- Opposite angles are equal,
- ∠ A = ∠ C = 90
- ∠ B = ∠ D = x
Now, in parallelogram,
Sum of angles = 360
∠ A + ∠ B + ∠ C + ∠ D = 360
90 + x + 90 + x = 360
180 + 2x = 360
2x = 360 - 180
2x = 180
x = 180/2
x = 90
So,
∠ A = ∠ B = ∠ C = ∠ D = 90
So, ABCD is a parallelogram with all angles 90
So, ABCD is a rectangle
Thus, parallelogram with one angle 90 is a rectangle.
Written on Oct. 17, 2017, 9:47 p.m.