Properties of Quadrilaterals: Parallelograms DO NOW 10/20: A classmate claims that the figure below is a rectangle. How can you prove that it is or isn’t? Properties of Quadrilaterals: Parallelograms Agenda Classifying Quadrilaterals Geogebra: Parallelograms Properties of Parallelograms Debrief A (3, 6) B (8, -1) C (-11, -4) D (-6, -11)

Polygons Polygon – three or more coplanar line segments, with every endpoint connected to another Examples Non-examples *MUST BE IN NOTES!*

Classifying Quadrilaterals

GeoGebra: Parallelogram On GeoGebra.org, click “Start Creating” and then click “Algebra.” Follow the steps on the sheet to construct a parallelogram. After Step 7, measure each angle and segment. Record your observations to the following in your notebook. What do we notice about the length of the sides? What do we notice about the measures of the angles? What do we notice about the slopes of the sides? EXIT TICKET: Take a screenshot of your completed parallelogram with Ctrl + and email to me at eben.witherspoon@uprepschools.com

Debrief: Properties of Parallelograms What do we notice about the length of the sides? What do we notice about the measures of the angles? What do we notice about the slopes of the sides?

Properties of Quadrilaterals: Rhombus DO NOW 10/21: Based on the construction below, what are the properties of a parallelogram? Properties of Quadrilaterals: Rhombus Agenda Pythagorean Theorem Construction: Rhombus Properties of a rhombus Debrief

Distance on the Coordinate Grid: Pythagorean Theorem Method *MUST BE IN NOTES!* Review: Pythagorean Theorem a2 + b2 = c2 c a b

Construction 3: Rhombus 1. Draw line segment AD (be sure to put both A and D on a coordinate!) Make a circle with center point A and radius with length AD. Make a point B on circle A somewhere above segment AD (be sure to put point B on a coordinate!) Using the SAME RADIUS, make another circle with center point B. Using the SAME RADIUS, make another circle with center point D. Make point C where circle B and circle D intersect. Connect segments AB, BC and CD to create your rhombus ABCD. 2. 3. 4. 5.

Gallery Walk: Properties of a Rhombus EXIT TICKET: Find the Side Lengths Plot the coordinates of A, B, C and D Use Pythagorean Theorem to find the length of the sides AB, BC, CD and AD of the rhombus. CHALLENGE PROBLEM (Yes, it is extra credit…): Diagonals – the line segments that connect non-consecutive vertices. Draw the diagonals AC and BD of the rhombus. Use the slope formula to make a hypothesis about the relationship between the diagonals of a rhombus.

Debreif: Think/Pair/Share In groups of 3: What are the properties of a rhombus? Write the properties and draw a picture of a rhombus on an post-it and place them on the Quadrilaterals Venn Diagram where you think they belong. Record the properties on your quadrilateral sheet.

Pythagorean Theorem and Distance Formula DO NOW 10/21: Use the Pythagorean Theorem to find the distance between two points on the coordinate grid. Pythagorean Theorem and Distance Formula Agenda HW Review Quadrilaterals Notes Deriving Distance Formula Debrief

HW Review

Classfying Quadrilaterals Notes

Deriving Formulas Deriving a formula means you are using prior knowledge to come up with a formula that works for a new situation. In your groups, using the Pythagoran Theorem manipulatives, derive an equation that will give you the distance using only coordinates. Questions to Consider: How can we find the length of the segment using Pythagorean Theorem? Other than counting “up and over,” what is another way we can find the length of a and b? (Hint: Think slope formula!) (3, 9) c a b (12, -2)

Derivation Carousel Each group will be given algebra manipulatives. Each group will start with the Pythagorean Theorem: a2 + b2 = c2 Each group will have ___ min. to develop a formula by substituting in coordinates (x, y) into the formula. One person stays at each group to explain work, all other group members continue on the next group. After ___ min., switch again. A NEW person will stay to explain, all other people at that group move on. Use Pythagorean Theorem and #7-14 on the HW sheet to test your formula to see if you get the same distance using both equations!

Debrief: Distance on the Coordinate Grid Pythagorean Theorem a2 + b2 = c2 Distance Formula (x2 – x1)2 + (y2 – y1)2 = d2 *MUST BE IN NOTES!* (x1, y1) c a b (x2, y2)

EXIT TICKET Use Pythagorean Theorem or Distance Formula to find the distance between the two points.

DO NOW 10/23: Find the distance between the coordinates DO NOW 10/23: Find the distance between the coordinates. A(7, -4) B(13, 8) Midpoint Formula Agenda HW Review Slope and Distance Quiz Midpoint Formula Embedded Assessment: Rollercoasters

HW Review

Slope, Distance and Quadrilaterals Quiz Using the coordinates (on top left of page) from the printed GeoGebra diagrams : Find the length of each side. Find the slope of each side. Based on your answers for #1-2, identify the type of quadrilateral. Explain how you know.

Midpoint Formula *MUST BE IN NOTES!* The midpoint is the point located at the average of the x and y values. (3, 9) M c a b (12, -2)

Debrief: Embedded Assessment Take Home Assignment: Answer #1-6 on a separate sheet - Use graph paper!) - Use rubric as a guide. Distance Fomula Slope Formula Midpoint Formula x y #1, 2 #4