1. Classifying Quadrilaterals: Trapezoids and Kites
Agenda:
HW Review
Properties GeoGebra Investigation
Quad with Algebra
Debrief
DO NOW 10/27: Based on the coordinates given, determine if the quadrilateral would be a rhombus or a rectangle. A (1, 3) B (2, 1) C (6, 3) D (5, 5)

2. Definition: Diagonals
A diagonal is a line segment that connects non-consecutive vertices.
*MUST BE IN NOTES!*

3. Quadrilateral Properties Investigation
Use the GeoGebra Workbook to complete your checklist of the properties of quadrilaterals.
Use the guiding questions under each as prompts. A property must ALWAYS be true of the shape, so move them around to be sure your property stays true.
You will earn 1 point for each accurate property and 1 additional point for each accurate property that no one else has identified.
Additional points will go as Extra Credit on last Thursday’s Quiz!

4. Properties of Kites and Trapezoids

5. Using Algebra with Properties of Quadrilaterals
STEPS
Identify the type of quadrilateral
Identify the property that you need to use
Set up the equation using your property and the given information.
Solve and check!

6. Exit Ticket: Quadrilateral Properties
Find the missing variable using the properties of quadrilaterals. 1. 2. 3.

7. Debrief: Coordinate Geometry
How do coordinates connect geometry and algebra?
What is the fastest way to use coordinates to determine the other properties of the shape?

8. Perimeter and Area of Quadrilaterals
Agenda:
HW Review
Review: Area and Perimeter
Area Formulas
Jigsaw: Perimeter and Area of Quadrilaterals
Debrief
DO NOW 10/27: Find the lengths of the diagonals of the quadrilateral below.

9. Review: Midpoint Midpoint Formula
Find the midpoint of the diagonals of square EFGH

10. Perimeter and Area of Quadrilaterals: Parallelograms
Perimeter: the sum of all of the sides
Ex. P = AB + BC + CD + DA
Area: the product of the two sides (length and width)
Ex. A = (AB) x (BC)
*MUST BE IN NOTES!*

11. Perimeter and Area of Quadrilaterals: Trapezoid
Perimeter: the sum of all of the sides
Ex. P = AB + BC + CD + DA
Area: the average of the bases times the perpendicular height
Ex. A = ½ (CD+AB)xDE
*MUST BE IN NOTES!*

12. Perimeter and Area of Quadrilaterals: Kite
Perimeter: the sum of all of the sides
Ex. P = AB + BC + CD + DA
Area: the average of the diagonals
Ex. A = ½ (AC)(DB)
*MUST BE IN NOTES!*

13. Perimeter and Area of Quadrilaterals: Practice
Perimeter: the sum of all of the sides
Area: the product of the two sides (length and width)

14. Perimeter and Area Jigsaw Appointments
1:00 – Find the length of sides AB and CD 2:00 – Find the length of sides BC and AD 3:00 – Find the length of diagonals AC and BD 4:00 – Find the midpoint of diagonals AC and BD 5:00 – Find the perimeter of quadrilateral ABCD 6:00 – Find the area of quadrilateral ABCD

15. Debrief: Area and Perimeter
What are the similarities and differences in the perimeter and area formulas for quadrilaterals?
How are the perimeter and area related?

16. Quadrilateral Properties
Agenda
Distance Quiz (6th&7th)
Jigsaw (Review)
Embedded Assessment (Review)
Quad Properties Practice
DO NOW 10/29: Use the properties of quadrilaterals to determine the value of the missing variables.

17. Distance Formula (Quiz 6th & 7th)

18. Properties of Quadrilaterals
Agenda
Quad Properties Review
Quad Properties Quiz
Intro to Transformations
Debrief
DO NOW 10/30:
Use quadrilateral properties to find the missing angle measures.

19. Properties of Quadrilaterals Practice

20. Properties of Quadrilaterals, Cont.

21. Intro to Rigid Transformations
Translations
47/Crowe/GeoGebra_Activity_3.html
Reflections
47/Crowe/GeoGebra_Activity_1.html
Rotations
47/Crowe/GeoGebra_Activity_2.html

22. Debrief: Transformations
What does it mean if a shape has undergone a “transformation”? What does it mean for a tranformation to be “rigid”?
In your own words, define “translation”, “reflection” and “rotation.”
How can you describe these transformations mathematically?

23. Transformations with Algebra
Agenda
HW Review/Note Check
Geogebra
Tranformations PPT (Notes)
Debrief
DO NOW 10/31: Which rigid transformation is shown below: rotation, reflection or translation. Explain your reasoning.

24. GeoGebra Investigation: Rigid Transformations/Isometries
Translations, Reflections and Rotations are all rigid transformations or “isometries.” This means that the resulting image after the transformation is congruent.
Questions to Consider:
What does it mean if a shape has undergone a “transformation”? What does it mean for a tranformation to be “rigid”?
In your own words, define “translation”, “reflection” and “rotation.”
How can you describe these transformations mathematically?

25. Intro to Rigid Transformations
Translations
47/Crowe/GeoGebra_Activity_3.html
Reflections
47/Crowe/GeoGebra_Activity_1.html
Rotations
47/Crowe/GeoGebra_Activity_2.html

26. Translations (5 minutes)
Translations are when an object “slides” or moves in a vertical or horizontal direction ( or a combination of both) on the coordinate grid.
To translate, we will add
or subtract to the
x and y values.
(x, y)  (x + a, y + a)

27. Translations
Write a rule to describe the translation

28. Reflections (5 minutes)
Reflections are when a figure is “reflected” or creates a mirror image of itself across the x or y axis, or some other line of symmetry
To reflect a figure, we
have to switch the signs
Across x-axis – switch y sign
(x, y)  (x, -y)
Across y-axis – switch x sign
(x, y)  (-x, y)
Across y = x – swap x and y
(x, y)  (y, x)

29. Lines of Symmetry (other than x- and y-axis)
If the equation is y=#, then the line is horizontal at that y-value.
If the equation is x=#, then the line is vertical at that x-value.
If there is some other equation, make an x/y table and find three points to create the line.

30. Find the Line of Symmetry
x = 3
y = -x

31. Reflection
Reflect the figure across the y=x

32. Rotations (5 minutes)
Rotation is where the figure “rotates” or turns on the coordinate grid a certain number of degrees (45˚, 90˚, etc.)
Every 90˚ we will
flip x and y and then use the
quadrant to determine signs.
(x,y)  (y,x) and find the signs

33. Quadrants
The coordinate grid can be broken up into 4 quadrants, based on the sign of the x and y values.
Q1 – (+,+)
Q2 – (-, +)
Q3 – (-, -)
Q4 – (+, -) Q2 Q1 Q3 Q4

34. Rotation
Rotate the triangle 90° clockwise about the origin

35. Debrief: Transformations
What does it mean if a shape has undergone a “transformation”? What does it mean for a tranformation to be “rigid”?
In your own words, define “translation”, “reflection” and “rotation.”
How can you describe these transformations mathematically?