Cyclic Quadrilateral Worksheet
Explore the properties of cyclic quadrilaterals, including theorems related to angles and diagonals, through a variety of problem types.
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Cyclic Quadrilateral Worksheet
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Read each question carefully and answer to the best of your ability. Show all your work for full credit.
1. Which of the following statements is true for any cyclic quadrilateral?
Opposite angles are complementary.
Opposite angles are supplementary.
All angles are equal.
Diagonals bisect each other.
2. If one angle of a cyclic quadrilateral is 80 degrees, what is the measure of its opposite angle?
80 degrees
90 degrees
100 degrees
180 degrees
3. A quadrilateral whose vertices all lie on a single circle is called a quadrilateral.
4. In a cyclic quadrilateral, the sum of each pair of opposite angles is equal to degrees.
5. Consider a cyclic quadrilateral ABCD inscribed in a circle. If angle A = 75 degrees and angle B = 110 degrees, find the measures of angle C and angle D. Show your work.
6. State Ptolemy's Theorem for a cyclic quadrilateral. Explain its significance.
7. A rectangle is always a cyclic quadrilateral.
True
False
8. A parallelogram that is not a rectangle can be a cyclic quadrilateral.
True
False
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