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)

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

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! http://tube.geogebra.org/student/b218943#material/29162

Properties of Kites and Trapezoids

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!

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

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?

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.

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

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!*

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!*

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!*

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

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

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?

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.

Distance Formula (Quiz 6th & 7th)

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.

Properties of Quadrilaterals Practice

Properties of Quadrilaterals, Cont.

Intro to Rigid Transformations Translations http://www.maa.org/sites/default/files/images/upload_library/ 47/Crowe/GeoGebra_Activity_3.html Reflections http://www.maa.org/sites/default/files/images/upload_library/ 47/Crowe/GeoGebra_Activity_1.html Rotations http://www.maa.org/sites/default/files/images/upload_library/ 47/Crowe/GeoGebra_Activity_2.html

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?

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.

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?

Intro to Rigid Transformations Translations http://www.maa.org/sites/default/files/images/upload_library/ 47/Crowe/GeoGebra_Activity_3.html Reflections http://www.maa.org/sites/default/files/images/upload_library/ 47/Crowe/GeoGebra_Activity_1.html Rotations http://www.maa.org/sites/default/files/images/upload_library/ 47/Crowe/GeoGebra_Activity_2.html

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)

Translations Write a rule to describe the translation

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)

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.

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

Reflection Reflect the figure across the y=x

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

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

Rotation Rotate the triangle 90° clockwise about the origin

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?