Question

Parallelogram ABCD is inscribed in a circle. Which properties of parallelograms and inscribed quadrilaterals can be used to prove that ABCD is a rectangle?

Answer 1

To prove that parallelogram ABCD is a rectangle, you can use the properties of both parallelograms and inscribed quadrilaterals.

Step-by-step explanation:

To prove that parallelogram ABCD is a rectangle, we can use the properties of both parallelograms and inscribed quadrilaterals. Here are the steps:

1. Since ABCD is a parallelogram, opposite sides are parallel and congruent. This means that AB is parallel to DC and AD is parallel to BC, and their lengths are equal.
2. Since ABCD is inscribed in a circle, we know that opposite angles are supplementary. This means that angle ABC + angle ADC = 180 degrees and angle ABD + angle BCD = 180 degrees.
3. Since ABCD is a parallelogram, opposite angles are congruent. This means that angle ABC = angle ADC and angle ABD = angle BCD.
4. Combining the properties of parallelograms and inscribed quadrilaterals, we can conclude that ABCD is a rectangle. In a rectangle, opposite sides are parallel and congruent, and opposite angles are congruent.