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.

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.

### 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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