Question

if one angle of a parallelogram is a right angle prove that all other angles are right angles​

Answer 1

Step-by-step explanation:

If one ange is right angle ,

the opposite one would be equal hence 90°.

Let parallelogram be ABCD,

<A = 90° (given)

<C = <A = 90° ( opposite)

<A+<B = 180° ( adjecent angles are supplementary)

<B = 90°

<D= 90° ( opposite to <B)

Hence ,

<A=<B=<C=<D=90°

Q.E.D.

Answer 2

Answer:

According to the properties of a parallelogram

The sum of the adjacent angles in the parallelogram should be supplementary to each other

So if one angle is a right angle the adjacent angle will also be a right angle.

The opposite angles of a parallelogram are equal in measure

So, if an angle is a right angle the opposite angle will also be a right angle.

Thus we can conclude that if one angle of a parallelogram is a right angle all other angles are also right angles​.

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