Lesson Plans ~ Mathematics CLG 2.2.3 ~ Concurrent Lines in Triangles ~ School Improvement in Maryland

Geometry, Measurement, & Reasoning |

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

Worksheet/Answer Key: Concurrent Lines in Triangles
Worksheet/Answer Key: Concurrent Lines in Triangles Chart
Worksheet/Answer Key: The Nine-Point Circle
Worksheet/Answer Key: Orthocenter Investigation
compass, straightedge, patty paper, Mira™
Heavy paper to create sturdy triangles that can be balanced without collapsing. Manila folders work well. Cut each folder along the crease. Give one side of a folder to each student. Encourage students to draw large triangles on their paper.

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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