I have students pair-up with a partner to explain how they can determine if four coordinate points form a parallelogram. This is a great Do Now to share out with the entire class as it gives students an opportunity to see a variety of approached to completing this proof as well as a chance to critique each others' reasoning (MP3).
This Do Now links well with the homework from the previous lesson, Proving Parallelograms. Although the expectations for completing the Do Now are different then the homework, students may want to use this homework assignment to guide them through the Do Now.
Students can use the Quads Presentation hand-out to fill in the information from other groups as they present on each shape. You can post the handout on the board and ask presenters to fill in the information as they present - or - assign each person in the group a role. One person could be the speaker, another the writer, another the person who answers any questions, etc. Depending on how involved and excited your students are this presentation process may take 15-25 minutes.
Depending on how much time is left in class, you can begin students notes work with students. This lesson will lead directly into the next day's class, Calling All Quads Again, so you should not expect to finish the entire lesson today.
In the beginning vocabulary section, how to prove each special quadrilateral, you can give students the opportunity to brainstorm together to fill in these sections. If time remains, students can work on the pair-share activity, which asks students to prove for coordinate points form a rhombus and not a rectangle. This is a complicated problem which asks students to pull together many concepts from this unit and persevere through a challenging task (MP1).
The last part of student notes, the Activity-Homework, could also become homework, if desired.