Entry Task Carly built a Ferris wheel using

Entry Task Carly built a Ferris wheel using her construction toys. The frame of the wheel is a regular 16 -gon. Find the sum of the angle measures of the Ferris wheel and the measure of one angle.

Properties of Parallelograms Lesson 6 -2

Learning Targets �I will be able to: �use the relationships among sides and angles of parallelograms to find side lengths and/or angle measures; �use the relationships among diagonals of parallelograms to find segment lengths and/or angle measures; �prove theorems about parallelograms.

Investigating Parallelograms �We are going to use the Chromebooks and Geogebra to investigate properties of parallelograms. �Go to the following link and investigate the sides and angles of a parallelogram. Click on the boxes for only the sides and angles and then drag points A, B, or D around to change the shape of the parallelogram. https: //www. geogebra. org/m/ST 3 C 9 abu Write at least 3 conjectures about the sides and angles of a parallelogram. Try to justify your conjectures.

What about the diagonals? �Click on the boxes “Diagonals” and the “Angle formed by Diagonals” in the investigation. Make sure all of the other boxes are not selected. �Are any of the angles formed by the diagonals congruent? If so, describe those angles and justify why they could be congruent. �Now click on the “Diagonals” and the “Parts of Diagonals” boxes only. �What do you notice about the lengths of the diagonals or the parts of the diagonals? Make a conjecture about the diagonals of a parallelogram and try to justify it.

Theorems about parallelograms If a quadrilateral is a parallelogram, then… �opposite sides are congruent. �consecutive angles are supplementary. �opposite angles are congruent. �diagonals bisect each other.

Examples 1. 2.

3.

Another related theorem: If three or more parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal.

4. If EF = FG= GH = 6 and AD = 15, what is CD?

Practice! Page 364 A: 9 -28 all B: 38 -41 all