The vertices of a quadrilateral are given by the coordinates . recall the four properties of parallelograms. Use coordinate geometry to prove that quadrilateral KAIT is a parallelogram. B 2x (y+49)° 2.0… In this case we have and. BetterLesson reimagines professional learning by personalizing support for educators to support student-centered learning. Later in the lesson, students will be using coordinate geometry to gather evidence that a quadrilateral satisfies the definition of  a parallelogram and possesses the properties of parallelograms. As a primer, I lead them through the Activating Prior Knowledge_Verifying Parallelogram Properties activity. One Pair of Opposite Sides are Both Parallel and Congruent Consecutive Angles in a Parallelogram are Supplementary We might find that the information provided will indicate that the diagonals of the quadrilateral bisect each other. In the student version I have left the coordinates blank so you can use some from the lessons you have already prepared. 4. DEGF. This foldable provides a quick an overview of the definiton and 5 theorems that may be used to prove a quadrilateral is a parallelogram. As they are working, I walk around making sure that students are measuring the right things and that they are documenting these measurements precisely. Impostors beware! Theorems. If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram. SWBAT use four different methods to prove that a quadrilateral defined by given vertex coordinates is a parallelogram. distance formula to establish congruent segments, and. Find the coordinates of the midpoint of the segment whose endpoints are H(6, 1) and K(8, 3). If a quadrilateral has one pair of sides that are both parallel and congruent. Way 2 : Show that a pair of opposite sides are congruent and parallel 4. There are a number of ways to show whether a quadrilateral placed on a coordinate plane is a parallelogram or not. Segment AB and segment CD have the same slope so they are parallel. Quadrilateral ABCD has coordinates A (3, −5), B (5, −2), C (10, −4), D (8, −7). WX(3, 5 , 5, 0 ,) ( ) ... One friend says the quadrilateral is a parallelogram but not a rectangle. Line CD and AB are equal in length because opposite sides in a parallelogram are are equal. I remind them that each of the three items on the handout asks them to make a final conclusion. 5) Quadrilateral JACK has vertices J(1,-4), A(10,2), C(8,5), and K(2,1). From algebra, remember that two lines are parallel if they have the same slope. Prove: The perimeter of rectangle . The segments also have the same length so they are congruent. 1. As I walk around, I am also looking for students with exemplary work who might present to the class. If you can prove that the quadrilateral fits the definition of a parallelogram, then it is a parallelogram. I give students 2 minutes to exchange papers with their A-B partners, give feedback, and make corrections. There are a number of ways to show whether a quadrilateral placed on a coordinate plane is a parallelogram or not. Prove a quadrilateral is a parallelogram in the coordinate plane. Segment AB and segment CD have the same slope so they are parallel. midpoint formula to determine if a segment has been bisected. Next I show a model response under the document camera that exemplifies the level of precision I want. proving a quadrilateral is a parallelogram. They are to show all calculations using precise notation (e.g. To close today's lesson I give students a chance to reflect on what they've done. Label your work and write a concluding statement. By the end of the activity, I want every student to know that coordinate geometry uses: I give students 15 minutes working in pairs to complete the activity. We can use the following Theorems to prove the quadrilateral are parallelograms. So they are bisecting each other. No; the slopes of line xy and xz are not opposite reciprocals. In other words, if the coordinate sum of the pairs of opposite vertices are the same it is a parallelogram. Tip: Take two pens or pencils of the same length, holding one in each hand. Show that both pairs of opposite sides are parallel 3. The midpoint of a segment in the coordinate plane with endpoints. Based on your measurements and calculations can you conclude that the quadrilateral is a parallelogram? In other words, if the midpoints of the diagonals are the same point, the quadrilateral is a parallelogram. In this lesson students learn to distinguish the real parallelograms from the pretenders. © 2020 BetterLesson. I also emphasize the importance of making precise measurements and documenting these measurements using precise notation (MP3). I give students 15 minutes to work independently on the Using Coordinates to Prove that a Quadrilateral is a Parallelogram handout. When the 15 minutes have elapsed, I announce that I will be selecting four students to present. Show algebraically that quadrilateral WXYZ is a parallelogram. is one half the perimeter of rectangle . Show two consecutive sides are congruent by distance formula 2x or 3.) Review Queue Write the converses of: the Opposite Sides Theorem, Opposite Angles Theorem, Consecutive Angles Theorem and the Parallelogram Diagonals Theorem. Therefore the diagonals of a parallelogram do bisect each other into equal parts. Do Now: ΔAFN: A(-7,6), F(-1,6), N(-4,2). Learn how to determine the figure given four points. It is easier, however, to use the Rhombus Corollary and simply show that all four sides of the quadrilateral are congruent. Both of these facts allow us to prove that the figure is indeed a parallelogram. I give students 5 minutes with their A-B partner to check their work and rehearse their presentations. AC is splitting DB into two segments of equal length. 3. He then then traveled west and stopped at a gas station to get air for his tire. There is a written explanation, a diagram, and an "if-then" statement under each tab.Perfect for interactive notebooks or as a stand alone graphic organizer. As they present I give specific praise related to the aesthetics and organization of students' work, their use of academic language, and the thoroughness of their narratives. Activating Prior Knowledge_Verifying Parallelogram Properties, Using Coordinates to Prove that a Quadrilateral is a Parallelogram. As students are working, I reveal the answers one at a time, being careful to lag behind where I see the majority of the students are on the handout. 1.) Prove that the quadrilateral MATH is a parallelogram. Use coordinates to prove simple geometric theorems algebraically. State the coordinates of point D such that quadrilateral ABCD is a square. Students are given 4 points. It may be easier to show that one of the angles is a right angle because we have already computed all of the slopes. In the previous section, students were oriented to the coordinate geometry methods they will need to use in this section. Show that both pairs of opposite sides are congruent. In this activity, we will use the Distance, Midpoint and Slope Formulas that we learned in Algebra 1 to show congruent, bisected and parallel segments. Use coordinate geometry to prove that MARY is a parallelogram. We can do this by showing that that the diagonals are congruent or by showing that one of the angles is a right angle. 166 The coordinates of the vertices of ABC are A (1,2), B (− 5,3), and C (− 6, − 3). Hence line CE and EB are equal and AE and ED are equal due to congruent triangles. "If a pair of opposite sides in a quadrilateral are parallel and congruent, then the quadrilateral is a parallelogram. Prove the triangle is isosceles, but not equilateral. To prove that it is a parallelogram, remember that the definition of a parallelogram is a quadrilateral with two pairs of parallel sides. In this lesson, students will be using the criteria to establish that quadrilaterals are parallelograms. Generalize about how you used coordinate geometry as a tool to achieve the goal. They must graph the 4 points and determine if they form a parallelogram. Prove that ABC is isosceles. As they are working, I walk around the classroom providing guidance to ensure that students are producing quality work that is correct. The other friend says the quadrilateral is a rectangle. Show that a pair of opposite sides are congruent and parallel Use Riley's definition to prove that ABCD is not an isosceles trapezoid. We can use the one of the following three ways to prove that quadrilateral is a rhombus. I have students write a paragraph responding to the following prompt: What was the main goal of the lesson today? Example Prove that the quadrilateral ABCD with the vertices in a coordinate plane A(-1,3), B(2,-1), C(8,1) and D(5,5) (see the Figure) is a parallelogram. This is an individual task and I ask students not to use their notes. select appropriate tools to gather the desired evidence. No matter how you change the angle they make, their tips form a parallelogram. Finally, I call the students up one at a time to present. If one pair of opposite sides of a quadrilateral are both parallel and congruent, then it’s a parallelogram (neither the reverse of the definition nor the converse of a property). Which statement explains how you could use coordinate geometry to prove that quadrilateral ABCD is a parallelogram? Joseph biked 8 miles north and stopped at Patsy's Peach Farm. #MTBoS30: Proving Parallelograms Pong For the first time, in Geometry I taught a lesson about proving quadrilaterals on the coordinate plane are parallelograms. Prove that both pairs of opposite sides are congruent. 2.) I explain that we will be gathering evidence to support the fact that these quadrilaterals are parallelograms. 2. Slope of segment AB = 2/5 as opposed to slope = 2/5 or just 2/5). Let's prove to ourselves that if we have two diagonals of a quadrilateral that are bisecting each other, that we are dealing with a parallelogram. So far in this unit, students have learned and proven properties of parallelograms. Therefore, one way to prove it is a parallelogram is to verify that the opposite sides are parallel. Here are a few ways: 1. Way 1 : We can use the definition and show that the quadrilateral is a parallelogram that has four congruent sides. Point A is at negative 3, 5. 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