CC Geometry H 1) One method to prove a quadrilateral is a parallelogram is to prove the diagonals bisect each other: Show that the diagonals have the same midpoint. 2.) Which statement explains how you could use coordinate geometry to prove that quadrilateral ABCD is a parallelogram? select appropriate tools to gather the desired evidence. Show that both pairs of opposite sides are parallel 3. B 2x (y+49)° 2.0… We can use the one of the following three ways to prove that quadrilateral is a rhombus. Generalize about how you used coordinate geometry as a tool to achieve the goal. 2. "If a pair of opposite sides in a quadrilateral are parallel and congruent, then the quadrilateral is a parallelogram. 2. They have also proven the criteria that are sufficient for proving a quadrilateral is a parallelogram. 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. Theorem 1 : If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram. To prove that it is a parallelogram, remember that the definition of a parallelogram is a quadrilateral with two pairs of parallel sides. Therefore the diagonals of a parallelogram do bisect each other into equal parts. Before we start, I remind students of the following: Then students begin working. So they are bisecting each other. Consider the quadrilateral ABCD. Based on your measurements and calculations can you conclude that the quadrilateral is a parallelogram? In this lesson, students will be using the criteria to establish that quadrilaterals are parallelograms. In this section of the lesson, students will be using coordinate geometry to prove that a quadrilateral is a parallelogram. Do Now: ΔAFN: A(-7,6), F(-1,6), N(-4,2). Once I've modeled a response, I give students 10 minutes to complete the rest of the activity independently. Activating Prior Knowledge_Verifying Parallelogram Properties, Using Coordinates to Prove that a Quadrilateral is a Parallelogram. If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram. It may be easier to show that one of the angles is a right angle because we have already computed all of the slopes. It is easier, however, to use the Rhombus Corollary and simply show that all four sides of the quadrilateral are congruent. If a quadrilateral has one pair of sides that are both parallel and congruent. Prove a quadrilateral is a parallelogram in the coordinate plane. There are a number of ways to show whether a quadrilateral placed on a coordinate plane is a parallelogram or not. Show that a pair of opposite sides are congruent and parallel If the diagonals of a quadrilateral bisect each other then the 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. recall the four properties of parallelograms. I like to get the students primed for the type of thinking they'll be required to do in the lesson. 1.) Show that a pair of opposite sides are congruent and parallel 4. I remind them that each of the three items on the handout asks them to make a final conclusion. They are only to use coordinate geometry. 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. Prove that the quadrilateral MATH is a parallelogram. The vertices of a quadrilateral are given by the coordinates . Use coordinate geometry to prove that MARY is a parallelogram. In other words, if the coordinate sum of the pairs of opposite vertices are the same it is a parallelogram. Way 1 : We can use the definition and show that the quadrilateral is a parallelogram that has four congruent sides. Now let's go the other way around. No; the slopes of line xy and xz are not opposite reciprocals. From algebra, remember that two lines are parallel if they have the same slope. I explain that for each item they must write a clear concluding statement that references the evidence they've gathered. 166 The coordinates of the vertices of ABC are A (1,2), B (− 5,3), and C (− 6, − 3). Quadrilateral ABCD has coordinates A (3, −5), B (5, −2), C (10, −4), D (8, −7). There are a number of ways to show whether a quadrilateral placed on a coordinate plane is a parallelogram or not. They must graph the 4 points and determine if they form a parallelogram. Line CD and AB are equal in length because opposite sides in a parallelogram are are equal. Students are given 4 points. distance formula to establish congruent segments, and. I give them 3 minutes to collect and document evidence. I give students 2 minutes to exchange papers with their A-B partners, give feedback, and make corrections. proving a quadrilateral is a parallelogram. 2. This foldable provides a quick an overview of the definiton and 5 theorems that may be used to prove a quadrilateral is a parallelogram. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, √3) lies on the circle centered at the origin and containing the point (0, 2). Find the coordinates of Y, such that, quadrilateral MARY is a parallelogram. I have students write a paragraph responding to the following prompt: What was the main goal of the lesson today? Next, I give an overview of the activity. To close today's lesson I give students a chance to reflect on what they've done. Write a My main goals for this activity are for students to: To get started, I give students one minute to fill in the four properties of parallelograms in the designated spaces on the handout. If you can prove that the quadrilateral fits the definition of a parallelogram, then it is a parallelogram. Give reason(s) why or why not. Segment AB and segment CD have the same slope so they are parallel. 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. midpoint formula to determine if a segment has been bisected. Segment AB and segment CD have the same slope so they are parallel. In this lesson students learn to distinguish the real parallelograms from the pretenders. The other friend says the quadrilateral is a rectangle. All Rights Reserved. In other words, if the midpoints of the diagonals are the same point, the quadrilateral is a parallelogram. SWBAT use four different methods to prove that a quadrilateral defined by given vertex coordinates is a parallelogram. I also emphasize the importance of making precise measurements and documenting these measurements using precise notation (MP3). Show that both pairs of opposite sides are congruent. DEGF. 4. In the student version I have left the coordinates blank so you can use some from the lessons you have already prepared. Therefore, one way to prove it is a parallelogram is to verify that the opposite sides are parallel. As a primer, I lead them through the Activating Prior Knowledge_Verifying Parallelogram Properties activity. WX(3, 5 , 5, 0 ,) ( ) ... One friend says the quadrilateral is a parallelogram but not a rectangle. 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. In this section, you will learn how to prove that a quadrilateral is a parallelogram. 5) Quadrilateral JACK has vertices J(1,-4), A(10,2), C(8,5), and K(2,1). Use of graph is optional. Theorems. Here are a few ways: Shape ABCD is shown. It has been illustrated in the diagram shown below. He then then traveled west and stopped at a gas station to get air for his tire. 3. Prove that your quadrilateral ABCD is … Hence line CE and EB are equal and AE and ED are equal due to congruent triangles. If you keep them parallel, no matter how you move them around, you can … Name: _____ Date: _____ 6.4 – Proving Quadrilaterals are Parallelograms Theorems to Prove Quadrilaterals are Parallelograms: If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram. ABCD is a parallelogram because segment AB is parallel and congruent to segment CD.". We can use the following Theorems to prove the quadrilateral are parallelograms. 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