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Lecture 8

MA 108 Lecture Notes - Lecture 8: Parallelogram, Quadrilateral, Moodle


Department
Mathematics
Course Code
MA 108
Professor
Elyse Suzanne Rogers
Lecture
8

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Geometry Honors Parallelogram Activity
Instructions: Make a copy of this document (File menu, Make a Copy). Rename your copy (File
menu, Rename) as “Parallelogram Activity (your name)” [for example, if your name is Clarence,
rename your copy as “Parallelogram Activity Clarence”]. Share it with Mr. Burke [click on the
blue Share button, in the Add people: box type larry.burke@ahs.acsgmail.net and allow him to
edit]. Do all of your work in this document. You may not share your document with any other
students, you may not copy to or from any other student’s document, and each student must
work on his or her own document. You may use any resources that you or your teammates can
find in Moodle or online to complete this activity.
Definition of a parallelogram: Find a definition of “parallelogram” and complete the following:
A parallelogram is…a simple quadrilateral with two pairs
of parallel sides.
Four characteristics of parallelograms: Open the Parallelogram Exploration in Moodle. You
will see a parallelogram ABCD with diagonals AC and BD intersecting at E, along with the
measures of the segments and angles in the sketch.
1) What do you notice about the opposite sides of ABCD (besides that they are parallel)? Verify
that this fact remains true no matter how you drag on the vertices of the parallelogram.
Answer: The lengths of the two opposite sides are always the same. Parallel sides are always
equal in length.
Write a paragraph proof of this fact. (Given parallelogram ABCD, use the definition of
parallelogram and alternate interior angles to show that triangle ABD is congruent to triangle
CDB, then use CPCTC.)
Angle EAB is congruent to angle ECD, and angle EAD is congruent to angle ECB by the AIA
theorem. Angle EBA is congruent to angle EDC, and angle EDA is congruent to angle EBC by the
AIA theorem as well. Segment DB is congruent to itself by the Reflexive POSC. Now, by using the
ASA shortcut, you can see that the two triangles are congruent. CPCTC proves that the opposite
sides of the parallelogram are congruent. The sides are congruent and so are the angles,
therefore the triangles in the parallelogram are congruent.
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