Download median of a trapezoid

Project AMP
Dr. Antonio R. Quesada – Director, Project AMP
Median of a Trapezoid
Key words:
Trapezoid, median
Summary:
Students will construct a trapezoid and its median, then investigate the relationship
between the median, bases and the angles formed.
Existing Knowledge:
It is assumed that the students will have been exposed to and are familiar with the
following terms: trapezoid, midpoint, median, corresponding angles, and consecutive
interior angles.
State Strand:
Geometry and spatial sense
NCTM Strand:
Analyze characteristics and properties of two-dimensional and three-dimensional
geometric shapes and develop mathematical arguments about geometric relationships.
Learning Objectives:
1. Construct a trapezoid and its median.
2. Investigate the relationship between the median and the two bases of a trapezoid.
3. Investigate the relationship between the angles of the trapezoid and the angles formed
by the median.
Materials:
Computer lab or set of calculators equipped with Cabri Geometry II and the lab
worksheet.
Procedures:
*Have students work in pairs to perform the following labs.
*Students will be assessed by turning in their lab sheets along with a copy of the
constructions made.
Project AMP
Dr. Antonio R. Quesada – Director, Project AMP
Median of a Trapezoid
Team Members:
File Name:
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Goal 1: Construct a trapezoid and its median.
Investigate using Cabri Geometry II
1. Construct AB .
(segment tool)
2. Construct point C not on AB
(point tool)
3. Construct a line through C that’s parallel to AB and label it m.
(parallel line tool)
4. Construct CD on line m
(segment tool)
5. Hide line m
(hide/show tool)
6. Construct two segments forming the legs of the trapezoid.
(segment tool)
7. Find the midpoint of the two legs of the trapezoid and name them X and Y.
(midpoint tool)
8. Construct XY
( XY is called the median of trapezoid ABDC)
Goal 2: Investigate the relationship between the median and the two bases of the
trapezoid.
1. Find the length of the 2 bases AB and CD
(distance and length tool)
2. Find the length of the median XY
3. Calculate ( BC + CD )/2
(Calculate tool)
How can you describe the relationship between the median and the bases?
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4. Construct a table that shows the lengths of AB , CD , XY , and ( AB + CD )/2
Project AMP
Dr. Antonio R. Quesada – Director, Project AMP
5. Select the pointer tool from the pointer toolbox. Drag the points A, B, C, or D to
manipulate the construction as you wish. Press the tab key to record additional values
in the columns. What do you observe as you manipulate the vertices of the trapezoid?
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Goal 3: Investigate the relationship between the angles of the trapezoid and the
angles formed by the median.
1. Measure all eight interior angles in the trapezoid and label them with the three
appropriate variables (use angle tool)
2. List all pairs of angles that are supplementary
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3. List all pairs of angles that are corresponding
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4.
List all pairs of consecutive interior angles
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