Lesson: Properties of Cyclic Quadrilaterals Mathematics

In this lesson, we will learn how to use cyclic quadrilateral properties to find missing angles and identify whether a quadrilateral is cyclic or not.

Lesson Plan

Students will be able to

  • identify the supplementary angles in a cyclic quadrilateral,
  • use the supplementary angles in a cyclic quadrilateral to solve problems including equations,
  • solve problems using the equality of the measure of an exterior angle of a cyclic quadrilateral and the measure of the interior angle at the opposite vertex,
  • identify when a quadrilateral is cyclic using the summation of two opposite angles,
  • identify when a quadrilateral is cyclic using the equality of the measure of an exterior angle and the measure of the interior angle at the opposite vertex.

Lesson Presentation

Lesson Video

Video Thumbnail
11:55

Lesson Explainer

Lesson Worksheet

Q1:

In the given figure, 𝑚∠𝐴𝑂𝐵=𝑑∘, 𝑚∠𝐵𝑂𝐷=𝑎∘, 𝑚∠𝐷𝑂𝐶=𝑏∘, and 𝑚∠𝐶𝑂𝐴=𝑐∘.

In terms of 𝑑, work out an expression for angles 𝐴𝐵𝑂 and 𝐵𝐴𝑂.

In terms of 𝑎, work out an expression for angles 𝐷𝐵𝑂 and 𝐵𝐷𝑂.

In terms of 𝑏, work out an expression for angles 𝐶𝐷𝑂 and 𝐷𝐶𝑂.

In terms of 𝑐, work out an expression for angles 𝐴𝐶𝑂 and 𝐶𝐴𝑂.

Find an expression for the sum of 𝑚∠𝐴𝐵𝐷 and 𝑚∠𝐴𝐶𝐷 in terms of 𝑎,𝑏,𝑐, and 𝑑, and simplify it fully.

Using what we know about the sum of angles around a point, what is the sum 𝑚∠𝐴𝐵𝐷+𝑚∠𝐴𝐶𝐷?

Q2:

Determine 𝑚∠𝐵𝐶𝐷.

Q3:

Find 𝑚∠𝐸𝑀𝑁, given that 𝐿𝑀𝑁𝐸 is a cyclic quadrilateral with 𝑚∠𝑀𝐿𝐸=64∘ and 𝑚∠𝑀𝐸𝑁=38∘.

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