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Lesson Plan: Lesson plans were written by Maryland mathematics educators and could be used when teaching the concepts.

Goal 2 Geometry, Measurement, And Reasoning

Expectation 2.1 The student will represent and analyze two- and three-dimensional figures using tools and technology when appropriate.

Indicator 2.1.2 The student will identify and/or verify properties of geometric figures using the coordinate plane and concepts from algebra.

Lesson Content

Application of Properties of Quadrilaterals in the Coordinate Plane

Objective

Students will be able to apply definitions and theorems to verify special quadrilaterals using coordinate geometry.

Approximate Time

One to two 45-minute lessons depending on the level of student you are working with. This is an excellent way to have students practice BCR's-for all levels of students.

Prerequisite Concepts Needed

Students should be able to apply the slope formula and be able to identify parallel or perpendicular lines after computing the slope. Students have been introduced to the properties of parallelograms. Usually the next section in geometry texts is proving a quadrilateral is a parallelogram and this lesson could serve as the next day's lesson after that introductory day.

Materials Needed

Lesson Structure

    Warm-Up/Opening Activity

    Worksheet: Warm-up
     
    Have students apply the slope formula. To save time you could have 5 groups, or if you have 5 rows of students, have each student do one then compile the information.
     
    Discuss which segments are parallel (having the same slope) and which segments are perpendicular (having slopes that are negative reciprocals). Also included for discussion are pairs of segments that have zero slope (horizontal) as well as undefined slope (vertical).

    Development of Ideas

    Key to the lesson: Today we are going to apply the slope formula, the midpoint formula, and the distance formula to justify that a given quadrilateral is a parallelogram.
     
    Worksheet: Quadrilaterals in the Coordinate Plane
     
    At this point, you may be nearing the end of class time and may give the following assignment: Verify ABCD is a parallelogram by choosing one pair of opposite sides and showing them parallel and congruent. Use mathematics to explain how you determined your answer. Use words, symbols, or both in your explanation.
     
    If you are not at the end of the period, you could verify ABCD is a parallelogram by showing that the diagonals bisect each other. (Show that both diagonals have the same midpoint, using the midpoint formula.)
     
    Extensions
    After investigating other quadrilaterals students could then: Verify parallelogram EFGH is a rectangle (or square, or rhombus). You could have groups of students use graph paper to plot a special quadrilateral then have them share the coordinates with another group. The second group could discover through application of properties the type of quadrilateral that is formed with the given coordinates. Students could show sides are perpendicular, using the slope formula or that the diagonals are congruent using the distance formula, or use other appropriate properties.
     
    Some students may prefer using a two column proof to justify today's work.

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