Question

If one of the angles of a parallalogram is a right angle,ptove that it is a rectangle​

Answer 1

Answer:

Step-by-step explanation:

Let ABCD be a parallelogram, in which angle A = 90°

Now angle A = angle C = 90° ( in a parallelogram opposite angles are equal )

Now AB is parallel to CD ( in a parallelogram opposite sides are parallel )

angle A + angle D = 180° ( co-interior angles )

angle D = 90°

angle B = angle D = 90° ( in a parallelogram opposite angles are equal )

As allangles are equal and are of 90° so ABCD is a rectangle.

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Answer 2

Answer:

opposite angles of a parallelogram are equal.

so,the angle opposite to the right angle is also 90.

Adjacent angles of a parallelogram are supplementary.

therefore, adjacent angle of the right angle is (180-90) = 90

Again, the angle opposite to it will also be 90.

Since all the angles of a parallelogram measure 90 , it is a rectangle