Lesson Content |
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| Different Methods of Construction
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Objective |
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| For the students to be able to perform geometric constructions using a variety of construction tools, investigate the properties of perpendicular bisectors and angle bisectors, and apply geometric constructions to real-life situations. |
Other Indicators Addressed |
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2.1.4 The student will construct and/or draw and/or validate properties of geometric figures using appropriate tools and technology.
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Approximate Time |
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| Two to three 50-minute lessons or one to two 90-minute lessons |
Prerequisite Concepts Needed |
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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 |
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Lesson Structure |
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Essential Questions |
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What are the measuring tools used in geometry?
How and when are these measuring tools used in geometry?
What are the construction tools used in geometry?
How and when are these construction tools used in geometry?
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Warm-Up/Opening Activity |
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Discuss how you would find the distance between two students in the classroom. Students should understand that distance is always measured as the shortest distance. The shortest distance between two points is the straight-line distance.
Discuss how you measure the distance from a student in the classroom to a wall of the classroom. Students should understand that the shortest distance between a point and a line (or a plane) is the perpendicular distance from the point to the line (or plane). |
Development of Ideas |
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| Discuss the appropriate uses of geometric construction tools.
A straightedge is only used for drawing line segments, not for measuring.
A compass can be used for drawing a circle with a given center and a given radius measured from that center or to copy a line segment or transfer a distance from one place to another.
Patty paper and Miras™ can be used to transfer distances or replicate congruent figures. They cannot be used for drawing circles.
Replicate a segment using the different geometric construction tools.
Worksheet: Review of Basic Constructions
Worksheet: Patty Paper Investigations
Determine right angles and perpendicular lines using patty paper. Questions 1-2
Determine distance using patty paper. Questions 3-6
Determine whether figures are congruent using patty paper. Question 7
Create congruent figures using patty paper. Question 8
Construct perpendicular lines and angle bisectors using patty paper.
Worksheet: Constructions Using Patty Paper
Construct perpendicular lines and angle bisectors using a compass and straight edge.
Worksheet: Constructions Using Compass and Straight Edge
Construct perpendicular lines and angle bisectors using a Mira.
Worksheet: Constructions Using Miras
Worksheet: Constructions
Note: This activity could be completed as a jigsaw activity. Students could complete one or two of the problems, assigned by the teacher. The students could then share their solutions with the class in the next lesson.
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