Geometry: Exploring Diagonals of Quadrilaterals

Objectives

• Demonstrate knowledge and understanding of the nature of different quadrilaterals based directly on the properties of their diagonals
• Identify quadrilaterals given only properties of their diagonals

Vocabulary

• diagonal
• vertex angles
• perpendicular bisector

About the Lesson

This lesson involves manipulating endpoints and/or the intersection point of two diagonals that have special characteristics. As a result, students will:

• Observe whether the two diagonals mutually bisect each other, bisect vertical angles, are congruent, or whether one is the perpendicular bisector of the other.
• Determine which special quadrilaterals can be formed and, in some cases, determine which special quadrilateral must be formed, based on what they know about the diagonals.