School Improvement in Maryland

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 2.2 The student will apply geometric properties and relationships to solve problems using tools and technology when appropriate.

Indicator 2.2.3 The student will use inductive or deductive reasoning.

Lesson Content

Concurrent Lines in Triangles

Objective

The student will investigate points of concurrency in triangles and apply these concepts to real-world situations.

Other Indicators Addressed

2.1.4 The student will construct and/or draw and/or validate properties of geometric figures using appropriate tools and technology.

Approximate Time

Two to three 50-minute lessons or one to two 90-minute lessons

Prerequisite Concepts Needed

Basic vocabulary: line, line segment, angle, ray, distance, congruence, perpendicular, bisector, midpoint, distance between two points, distance between a point and a line, median of a triangle, altitude of a triangle
 
Students should understand the relationship of a figure and its image after a reflection over a line.

Materials Needed

Lesson Structure

    Essential Questions

    How can the properties of angle bisectors, perpendicular bisectors, and concurrent lines be applied to real-world situations?

    Warm-Up/Opening Activity

    Review or define the following terms:
    Median of a triangle
    Altitude of a triangle
    Concurrent lines

    Development of Ideas

    Construct and investigate the properties of concurrent lines in a triangle.
     
    Divide the students into groups of 3. Assign each student in the group only one type of triangle (acute, right, or obtuse) to investigate.
    Worksheet: Concurrent Lines in Triangles
     
    Summarize the properties of concurrent lines in acute, right, and obtuse triangles.
    Worksheet: Concurrent Lines in Triangles Chart
     
    Supplemental Activities/Resources
     
    Investigate properties of the orthocenter using technology
    Worksheet: The Nine-Point Circle
    Worksheet: Orthocenter Investigation

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