1­ Quadrilaterals.notebook
May 18, 2016
Geometry­ Day 1: Defining, Sorting, and Classifying Quadrilaterals Let's start off with a basic question; What is a quadrilateral?
1­ Quadrilaterals.notebook
May 18, 2016
How many different TYPES of quadrilaterals can you name/draw in 5 minutes? GO!
1­ Quadrilaterals.notebook
Types we will focus on:
Parallelogram
Square
Rectangle Rhombus
Kite
Trapezoid
*Complex
May 18, 2016
1­ Quadrilaterals.notebook
May 18, 2016
Ways we can sort Quadrilaterals
A: Sides
True, all quadrilaterals have 4 sides, but we can look at side properties in more detail than that.
1. Are any sides parallel? (if so, how many sets?)
2. Are any sides congruent? (if so, how many sets?)
1­ Quadrilaterals.notebook
Side Scavenger Hunt
­Find a quadrilateral with:
­ no pairs parallel sides and no congruent sides
­ 1 pair of parallel sides and no pairs of congruent sides
­ 2 pairs of parallel sides and no pairs of congruent sides
­ no pairs of parallel sides and 2 pairs of congruent sides
­1 pair of parallel sides and 2 pairs of congruent sides
­2 pairs of parallel sides and 2 pairs of congruent sides
­no pairs of parallel sides and all sides congruent
­1 pair of parallel sides and all sides congruent
­2 pairs of parallel sides and all sides congruent
May 18, 2016
1­ Quadrilaterals.notebook
May 18, 2016
1­ Quadrilaterals.notebook
May 18, 2016
Ways We Can Sort Quadrilaterals
B: Angles We know that all quadrilaterals have 4 angles, but we can look at angle properties in more detail. ­All the interior (inside angles) for each quadrilateral have to add up to a specific number. What is is?
­Some quadrilaterals have 4 equal angles
­Some quadrilaterals have opposite angles that are equal
What are opposite angles?
­Some quadrilaterals have adjacent angles that are equal
­Some quadrilaterals have no equal angles **Can you create an example of each?
What are adjacent angles?
1­ Quadrilaterals.notebook
May 18, 2016
*depends on type of trapezoid
1­ Quadrilaterals.notebook
May 18, 2016
1­ Quadrilaterals.notebook
Ways we can sort quadrilaterals
C: Lines of Symmetry
A line of symmetry is a line that splits the shape into 2 equal halves
­Lines of symmetry can be horizontal, vertical, and diagonal
**quadrilaterals can have between 0 and 4 lines of symmetry. *How many does each of your quadrilaterals have? http://www.mathsisfun.com/geometry/symmetry­line­plane­
shapes.html
May 18, 2016
1­ Quadrilaterals.notebook
May 18, 2016
1­ Quadrilaterals.notebook
Ways we can sort quadrilaterals D: Diagonals Diagonal­ a line between two vertices of a polygon that do not share a side
There are 3 types of diagonals: 1) Mutually Bisecting­ diagonals that cut each other in half
2) Perpendicular­ diagonals that form four 90 degree angles when they meet
3) Perpendicular Bisecting­ diagonals that form four 90 degree angles AND cut each other in half
https://math.okstate.edu/geoset/Projects/Ideas/QuadDiags.htm
May 18, 2016
1­ Quadrilaterals.notebook
May 18, 2016
Paper Strips for Diagonals activity
In groups, use the paper strips and fasteners to see if you can create each quadrilateral included in the chart. Then use each created shape to fill out the rest of the chart.
1­ Quadrilaterals.notebook
Quadrilateral
May 18, 2016
Sketch
Length of Diagonals
Mutually Bisecting Diagonals?
Perpendicular Diagonals?
Rectangle
same
yes
no
Trapezoid
same or different
no
no
Parallelogram
same or different
yes
no
different
yes
yes
same or different
no
yes
same
yes
yes
Rhombus
Kite
Square