Question

question 2 of 10

a ______ is the only parallelogram that can be inscribed in a circle.

a. rhombus
b. trapezoid
c. rectangle
d. triangle

Explanation:

Analyze inscribed quadrilateral properties

An inscribed quadrilateral must have opposite angles that sum to \(180^\circ\).

$$ \angle A + \angle C = 180^\circ,\quad \angle B + \angle D = 180^\circ $$

Apply properties to a parallelogram

In a parallelogram, opposite angles are equal.

$$ \angle A = \angle C,\quad \angle B = \angle D $$

Combining these properties:

$$ 2\angle A = 180^\circ \implies \angle A = 90^\circ $$

$$ 2\angle B = 180^\circ \implies \angle B = 90^\circ $$

Identify the specific quadrilateral

A parallelogram with four right angles is a rectangle.

$$ \text{Parallelogram with } 90^\circ \text{ angles} = \text{Rectangle} $$

Answer:

• A. rhombus
• B. trapezoid
• C. rectangle (Correct answer)
• D. triangle