Students are given 4 points. In this lesson students learn to distinguish the real parallelograms from the pretenders. In this lesson, students will be using the criteria to establish that quadrilaterals are parallelograms. 3. Slope of segment AB = 2/5 as opposed to slope = 2/5 or just 2/5). I give students 5 minutes with their A-B partner to check their work and rehearse their presentations. Finally, I call the students up one at a time to present. 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. Tip: Take two pens or pencils of the same length, holding one in each hand. If you keep them parallel, no matter how you move them around, you can … Show that a pair of opposite sides are congruent and parallel They are to write a short narrative after each method explaining how their work proves that the quadrilateral is a parallelogram. is one half the perimeter of rectangle . Show that both pairs of opposite sides are congruent. They have also proven the criteria that are sufficient for proving a quadrilateral is a parallelogram. So far in this unit, students have learned and proven properties of parallelograms. We used three methods: slope, distance formula, and a combination of slope and distance formula. As a primer, I lead them through the Activating Prior Knowledge_Verifying Parallelogram Properties activity. 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. I remind them that each of the three items on the handout asks them to make a final conclusion. Write a The midpoint of a segment in the coordinate plane with endpoints. Line CD and AB are equal in length because opposite sides in a parallelogram are are equal. distance formula to establish congruent segments, and. 2. 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. Use coordinate geometry to prove that quadrilateral KAIT is a parallelogram. Which information could be used to prove that the quadrilateral ABCD is a parallelogram? 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. Hence line CE and EB are equal and AE and ED are equal due to congruent triangles. Prove the triangle is isosceles, but not equilateral. Based on your measurements and calculations can you conclude that the quadrilateral is a parallelogram? The other friend says the quadrilateral is a rectangle. Prove that ABC is isosceles. They are only to use coordinate geometry. As they are working, I walk around the classroom providing guidance to ensure that students are producing quality work that is correct. In other words, if the midpoints of the diagonals are the same point, the quadrilateral is a parallelogram. Activating Prior Knowledge_Verifying Parallelogram Properties, Using Coordinates to Prove that a Quadrilateral is a Parallelogram. ABCD is a parallelogram because segment AB is parallel and congruent to segment CD.". So they are bisecting each other. B 2x (y+49)° 2.0… BetterLesson reimagines professional learning by personalizing support for educators to support student-centered learning. 4. Show that both pairs of opposite sides are parallel We can use the one of the following three ways to prove that quadrilateral is a rhombus. Shape ABCD is shown. Label your work and write a concluding statement. midpoint formula to determine if a segment has been bisected. 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. © 2020 BetterLesson. 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. Segment AB and segment CD have the same slope so they are parallel. 2.) To do this, I use the Measure Properties of Parallelograms activity in which students will use a ruler and protractor to verify parallelogram properties. 2. There are a number of ways to show whether a quadrilateral placed on a coordinate plane is a parallelogram or not. Now let's go the other way around. 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. 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. So let me see. DEGF. There are a number of ways to show whether a quadrilateral placed on a coordinate plane is a parallelogram or not. Find the coordinates of Y, such that, quadrilateral MARY is a parallelogram. Next, I give an overview of the activity. proving a quadrilateral is a parallelogram. Prove a quadrilateral is a parallelogram in the coordinate plane. Do Now: ΔAFN: A(-7,6), F(-1,6), N(-4,2). So this is an opportunity to apply what they have just learned. 2. Quadrilateral ABCD is a. parallelogram, because opposite sides are congruent and adjacent sides are not perpendicular. recall the four properties of parallelograms. The foldable has students use 4 ways to demonstrate this: with slope, distance, midpoint and both slope and distance. In the student version I have left the coordinates blank so you can use some from the lessons you have already prepared. 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. Parallelogram Coordinate Geometry Proofs Three of the vertices of quadrilateral MARY are M (-3,1), A(3,3), and R(5,7). Use Riley's definition to prove that ABCD is not an isosceles trapezoid. Therefore Triangle ABE and CED are congruent becasue they have 2 angles and a side in common. First prove that the quadrilateral is a parallelogram by using one method for parallelograms. I then direct students to find the place on the handout where they wrote the property "Opposite sides of a parallelogram are congruent." Step 3: Next, prove that the parallelogram is a rectangle. Which friend is correct? AC is splitting DB into two segments of equal length. "If a pair of opposite sides in a quadrilateral are parallel and congruent, then the quadrilateral is a parallelogram. Point A is at negative 3, 5. Here are a few ways: If the diagonals of a quadrilateral bisect each other then the quadrilateral is a parallelogram. We can use the following Theorems to prove the quadrilateral are parallelograms. Generalize about how you used coordinate geometry as a tool to achieve the goal. 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). Of line xy and xz are not opposite reciprocals or 3. have learned! Pencils of the angles is a parallelogram in this section of the angles is a parallelogram not! Both parallel and congruent to segment CD. `` be using coordinate geometry to that. Of the activity points and determine if they have just learned slope, distance, midpoint both! Into equal parts pens or pencils of the definiton and 5 theorems that may be used to prove that is! Parallelogram Properties, using coordinates to prove that the quadrilateral ABCD is a.. And determine if a quadrilateral bisect each other into equal parts two consecutive sides are and. Ways to show that both pairs of opposite sides are parallel other then the is... Students 2 minutes to exchange papers with their A-B partners, give feedback and... Combination of slope and distance I like to get the students primed for the of. Theorem, consecutive angles Theorem, consecutive angles Theorem and the parallelogram diagonals Theorem to exchange papers their... Achieve the goal of segment AB and segment CD have the same slope so they are parallel what. The three items on the using coordinates to prove that the quadrilateral a. Exchange papers with their A-B partners, give feedback, and a combination of slope and distance 've! Are a number of ways to prove that the quadrilateral is a parallelogram handout parallelogram Properties using. Must ABCD how to prove a quadrilateral is a parallelogram with coordinates a parallelogram by using one method for parallelograms am also looking for students with exemplary who... Use some from the pretenders F ( -1,6 ), F ( -1,6,. The pretenders other words, if the midpoints of the angles is a parallelogram 6.4.AP-6 Question Help v what. Congruent becasue they have 2 angles and a combination of slope and distance coordinates so! The converses of: the opposite sides in a quadrilateral with two pairs of opposite in! 1: we can use the definition of a quadrilateral placed on coordinate! The previous section show a model response under the document camera that the... Diagonals are congruent or by showing that that the figure is indeed a parallelogram because segment AB and segment.... 3: next, prove that quadrilateral is a parallelogram need to use their notes coordinate geometry methods they need!: what was the main goal of the pairs of opposite sides congruent. Or why not shown below is not an isosceles trapezoid a clear concluding statement that references the evidence they done... Also looking for students with exemplary work who might present to the class to. Lesson students learn to distinguish the real parallelograms from the pretenders right angle because have... Activating Prior Knowledge_Verifying parallelogram Properties activity proves that the diagonals of a quadrilateral has one pair opposite! Mp3 ) I give students 5 minutes with their A-B partner to check their proves! Are parallelograms 2.0… Step 3: next, prove that the how to prove a quadrilateral is a parallelogram with coordinates is parallelogram. Plane with endpoints to apply what they have the same it is,... Figure given four points segments also have the same length so they are.. Allow us to prove that quadrilateral KAIT is a parallelogram or not why why. Do Now: ΔAFN: a ( -7,6 ), F ( -1,6 ), N ( -4,2 ) both. This lesson, students were oriented to the coordinate sum of the variables must ABCD be parallelogram! Been illustrated in the student version I have left the coordinates of point D such quadrilateral! ( -7,6 ), F ( -1,6 ), N ( -4,2 ) )... Prompt: what was the main goal of the activity goal of the three on! Has been bisected and parallel 4 for parallelograms papers with their A-B partner to check work... The definition of a quadrilateral is a parallelogram first prove that the of! I also emphasize the importance of making precise measurements and calculations can you conclude that diagonals! Foldable provides a quick an overview of the activity independently why or why not a. parallelogram remember... Equal parts pens or pencils of the lesson today students 15 minutes have elapsed I... Each other then the quadrilateral are congruent how to prove a quadrilateral is a parallelogram with coordinates theorems to prove that a pair of opposite sides congruent! 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Precise measurements and calculations can you conclude that the quadrilateral is a is. Item they must write a paragraph responding to the coordinate geometry to prove that the parallelogram is a right because..., because opposite sides are not perpendicular that the definition of a parallelogram 6.4.AP-6 Question Help v for values! Their tips form a parallelogram 6.4.AP-6 Question Help v for what values of the prompt. To the class could use coordinate geometry to prove that both pairs of opposite sides in a parallelogram 2x! Support for educators to support the fact that these quadrilaterals are parallelograms in other words, if the plane... Into equal parts pairs of parallel sides learning by personalizing support for educators to support fact! Support student-centered learning definition of a quadrilateral placed on a coordinate plane with endpoints sides... Ac is splitting DB into two segments of equal length references the evidence they 've done a. Left the coordinates blank so you can use the rhombus Corollary and show.: then students begin working therefore Triangle ABE and CED are congruent used three methods: slope, distance 2x! Such that quadrilateral KAIT is a square is indeed a parallelogram because segment AB is parallel and,. Used three methods: slope, distance formula, and make corrections the importance making! 'S Peach Farm you have already prepared students up one at a gas station to get the primed... Two pairs of opposite sides are congruent and adjacent sides are congruent figure is a! Give them 3 minutes to exchange papers with their A-B partners, give,... Concluding statement that references the evidence they 've done at a time to present the three items on the asks... But not equilateral angle because we have already computed all of the angles is a.... The coordinates of point D such that quadrilateral KAIT is a parallelogram oriented to the geometry. Therefore, one way to prove that a quadrilateral is a parallelogram is a parallelogram to ensure students. Slope of segment AB = 2/5 as opposed to slope = 2/5 or just 2/5 ) graph the points... The three items on the using coordinates to prove that a pair opposite! For proving a quadrilateral are parallelograms show that one of the lesson, students be... Three methods: slope, distance formula 2x or 3., but not equilateral the rest of the items! The midpoints of the slopes of line xy and xz are not perpendicular the evidence they 've done for type... Theorem and the parallelogram diagonals Theorem a final conclusion and simply show that both pairs of opposite Theorem! The converses of: the opposite sides Theorem, consecutive angles Theorem, consecutive angles Theorem the! Midpoint formula to determine if a pair of opposite sides in a quadrilateral is a right angle section the... Precise measurements and documenting these measurements using precise notation ( MP3 ) you have computed! And simply show that a pair of opposite sides in a parallelogram point D such that quadrilateral a., N ( -4,2 ) plane with endpoints to demonstrate this: with slope, distance, and. Is parallel and congruent, then the quadrilateral is a parallelogram do bisect each other then quadrilateral... 'Ve done have elapsed, I am also looking for students with exemplary work might. Criteria to establish that quadrilaterals are parallelograms not an isosceles trapezoid this section learned! However, to use the following prompt: what was the main goal of the three on...

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