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Cyclic Quadrilaterals

Activity Overview

Students construct cyclic quadrilaterals and investigate their properties. They determine which quadrilaterals from the quadrilateral hierarchy are cyclic.

Before the Activity

  • See the attached PDF file for detailed instructions for this activity
  • Print page 19 from the attached PDF file for your class

    • During the Activity

    Distribute the page to the class.

    Follow the Activity procedures:

  • Construct a circle and label its center
  • Inscribe a quadrilateral within the circle
  • Note that the opposite interior angles are supplementary and the perpendicular bisectors of the sides of the quadrilateral are concurrent at a point if, and only if, the quadrilateral is cyclic
  • Measure the lengths of the sides and diagonals of the quadrilateral
  • Observe that the sum of the products of the two pairs of opposite sides is equal to the product of the diagonals
  • Determine which quadrilaterals from the quadrilateral hierarchy can be cyclic
  • Understand that if a parallelogram is cyclic, it has to be a rectangle, and if a rhombus is cyclic, it has to be a square
  • Verify the formula for determining the area of a cyclic quadrilateral

    • After the Activity

    Review student results:

  • As a class, discuss questions that appeared to be more challenging
  • Re-teach concepts as necessary

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