Question

7. If one angle of a parallelogram is a right angle, prove that it is a rectangle.
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Answer 1

Answer:

Step-by-step explanation:

onsider ABCD be a parallelogram and measure of angle C is 90°.

Now, since ABCD is a parallelogram, then measure of angle will be equal to measure of angle A, that is

m∠C=m∠A=90° (Opposite angles of parallelogram are equal)

and m∠A+m∠B=180 (Corresponding angles)

⇒90+m∠B=180

⇒m∠B=90

Also, m∠B=m∠D=90°(Opposite angles of parallelogram are equal)

Thus, m∠A=m∠B=m∠C=m∠D=90°.

Since, all the angles of the parallelogram are equal to 90, therefore ABCD is a rectangle, by the properties of rectangle.

Hence proved.

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