Special Parallelogram Properties
Overview
Students investigate parallelogram properties to figure out which properties apply to special parallelograms.
Special Parallelogram Properties
Parallelogram Properties
Task: Drawing a square, rectangle, parallelogram, and rhombus, students investigate to figure out which properties of quadrilaterals apply to which figures.
Tools Needed: Pencil, Graph Paper, Protractor, and a Ruler
Standards:
G.GCO.10* Prove, and apply in mathematical and real-world contexts, theorems about parallelograms, including the following: a. opposite sides of a parallelogram are congruent; b. opposite angles of a parallelogram are congruent; c. diagonals of a parallelogram bisect each other; d. rectangles are parallelograms with congruent diagonals; e. a parallelograms is a rhombus if and only if the diagonals are perpendicular
Plan: In my class, we take one of the four main quadrilaterals a day and go through checking off which properties they have. I want my kids to be investigators instead of just handing them the properties. We start with discussing basic properties of quadrilaterals and then move through the order of parallelogram, rectangle, rhombus, and finally square. I give my kids a copy of the chart attached and then the following equations.
On graph paper, the students are to graph the following:
Parallelogram: y=6, y=(-1), y=2x-7, y=2x+5
Rectangle: y=3x-2, y=3x+7, y=(-⅓)x, y=(-⅓)x+9
Square: y=2x+4, y=2x-3, y=(-½)x+1, y=(-½)x +(9/2)
Rhombus: I usually change it up a bit for a rhombus and instead tell them to plot the following points. (-1,0), (-4,-4), (-1,8), and (2,4). This provides extra practice for students with having to find the slopes and equations of the lines.
Using the chart attached, a ruler, and a protractor, have the students measure and decide which properties go along with which quadrilaterals.