After spending time learning about our favorite three-sided polygon – triangles – it’s only natural that we move on to quadrilaterals. This unit is mainly about learning the properties of quadrilaterals, with a dash of proofs thrown in for good measure. Read more to learn more about how I teach quadrilateral properties using interactive notebooks in high school geometry.
Parallelogram Properties
We begin our unit with everyone’s favorite quadrilateral – the parallelogram. For this unit, the notes are divided by definition or property. (Honestly, it’s like that for most units, but it is very obvious in this one.) We define a parallelogram, we talk about a property, and then there’s practice examples. We define another property, and then there are more practice examples. I like to use that separation. First of all, it makes it easier for students to understand. One property at a time. Secondly, it makes it easier for students to refer back to. When (or if) they look at their notes later, they can see very clearly how each property is applied.
To practice parallelograms, I like to use a self-checking Google Sheets digital activity. It allows students the chance see if they make any mistakes right away. Which is helpful considering all of the properties that can be applied with parallelograms.
Properties of Quadrilaterals: Special Parallelograms
This is where my students struggle. Parallelograms, we’re good. Rhombuses, rectangles, and squares too? Now we’re in trouble. This unit is a lot. A lot of shapes, a lot of properties, and a lot of memorization. For the special parallelograms, I teach each one on a separate day. We take the notes for rhombuses, and then we practice them. We do the same for rectangles and squares. What I’ve seen teachers traditionally do for this topic is teach them all at once. I did that my first year, and it was a big mistake. Students were so confused, and struggled to correctly identify which property belonged to which shape. Even with them taught separately, students still struggle. To help students, I like to incorporate as much practice as possible on identifying properties of each quadrilateral. Throughout these lessons, we refer to the quadrilateral properties chart students keep in their interactive notebooks.
To help students focus on one special parallelogram at a time, I also like to have separate practice opportunities. This year I used a separate Google Form to practice each shape: Rhombuses, Rectangles, & Squares.
Trapezoid Quadrilateral Properties
The bulk of our lesson on trapezoids is on isosceles trapezoids. We start by defining trapezoids, and we apply their only property. So, we quickly move on to the isosceles trapezoids in the same lesson. Along with the definition, we analyze the anatomy of an isosceles trapezoid. Then, we are able to apply its quadrilateral properties with practice examples.
Midsegments of Trapezoids
The next day, we learn about the midsegments of trapezoids. (I’ve also seen this referred to as the median of trapezoids.) Midsegments gets its own day because it would be too much with the previous lesson. After the definition and theorem, we derive formulas to find the midsegments of trapezoids. We usually do a quick compare and contrast with our previous lesson on midsegments of triangles. For this theorem, I like to show my students two formulas. The traditional formula, that takes one half of the bases, and an alternate formula that instead doubles the midsegment. Since the formula includes two bases, the equations for this topic can be a bit cumbersome for my students. The alternate formula helps the students that would be overwhelmed otherwise.
Parallelogram Proofs
For our lesson on parallelogram proofs, we focus on proving triangles formed within parallelograms are congruent, and proving that quadrilaterals are parallelograms. We also incorporate special parallelograms into these proofs. Together we complete 3 proofs for our notes, taking time to talk about how to prove a quadrilateral is a parallelogram. Then, we do independent practice with proof cards. Proof cards allow students to complete proofs (from a packet) with a set of cards that contain hints to completing proofs. I’ve found this method of proof practice to increase independence in students much faster than the traditional methods of proof practice. For more information about proof cards, you can read my previous post about them.
Quadrilateral Properties Unit: Other Topics
What about kites? I don’t teach them, but I do have an interactive notebook page dedicated to them if you need it.
Also, this is typically the unit where geometry teachers teach about the polygon interior and exterior angles theorem. It is very enneagram type 1 of me, but I can’t put a polygon lesson inside the quadrilaterals unit. Instead, I teach this topic as a standalone lesson at the beginning of the year. (It’s also a great way to confirm that students walked into my classroom with the knowledge that the interior angles of a triangle sum to 180 degrees.) You can see what I mean by checking out my Sum of Interior Polygons notebook page.
Are you teaching a unit on quadrilaterals properties? You can get everything you need for a geometry interactive notebook quadrilaterals unit in both print and digital versions.
