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**preview**shows half of the first page. to view the full**3 pages of the document.**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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