Question

question 1 of 25 true or false? if a circle is circumscribed about a parallelogram, the parallelogram must be a rectangle. a. true b. false

Explanation:

Step1: Recall property of cyclic quadrilaterals

In a cyclic quadrilateral (a quadrilateral inscribed in a circle), the sum of opposite angles is 180°.

Step2: Consider properties of parallelograms

In a parallelogram, opposite angles are equal. Let the opposite angles be $\angle A$ and $\angle C$, $\angle B$ and $\angle D$. So $\angle A=\angle C$ and $\angle B = \angle D$.

Step3: Use the cyclic - quadrilateral property

Since the parallelogram is cyclic, $\angle A+\angle C = 180^{\circ}$ and $\angle B+\angle D=180^{\circ}$. Because $\angle A=\angle C$, then $2\angle A = 180^{\circ}$, so $\angle A = 90^{\circ}$. Similarly, $2\angle B=180^{\circ}$, so $\angle B = 90^{\circ}$. A parallelogram with one - right angle is a rectangle.

Answer:

A. True