# proving quadrilaterals are parallelograms activity

Proving Quadrilaterals are Parallelograms PROVING QUADRILATERALS ARE PARALLELOGRAMS The activity illustrates one way to prove that a quadrilateral is a parallelogram. Activity Checklist. I explain that we'll be writing four proofs that quadrilaterals are parallelograms and that these four proofs will differ only in terms of the information that is given. Proofs of general theorems. One pair of opposite sides are parallel. There are six important properties of parallelograms to know: Opposite sides are congruent (AB = DC). D. Both pairs of opposite angles are congruent. Foldable perfect for notebooks covering the different methods used to prove a quadrilateral to be a parallelogram using coordinate geometry. Donate or volunteer today! Alright Euclideans now the real challenge begins. So, we have. This is meant to be a culminating assignment after the completion of your study of geometric quadrilaterals. To play this quiz, please finish editing it. The distance formula given above can be written as: This is precisely the Pythagorean Theorem if we make the substitutions: , and .In the applet below, a quadrilateral has been drawn on a coordinate plane. Geometry - Prove Quadrilaterals are Parallelograms Let us now prove this result. Triangles can be used to prove this rule about the opposite sides. C. Both pairs of opposite sides are congruent. These include re-reading, making connections between narrative and diagram, and understanding the sequencing of statements. Notes on Quadrilateral. This five question Google Form will help you to pinpoint who's struggling and where.This mini assessment is designed for students to turn in/upload the work to you...and o. B. Opposite angels are congruent (D = B). Parallelograms: IM 6.1.4. – All internal angles are of “right angle” (90 degrees). In the Solve It, you used angle properties to show that lines are parallel. I also pause to think-pair-share whenever there are blanks on the handout for students to fill in. When at least 85 percent of the students have a completed proof, I look for two or three exemplars that are thorough, precise and clear and these students come up to the front to present their proofs. Please let me know if you need assistance. Lesson 16-1 PLAN Materials • whiteboard or … A. Proving Quadrilaterals are Parallelograms. I insert pauses as needed to discuss important concepts that should not be glossed over. This activity allows students to have an open discussion with their peers and their teacher about their level of understanding of properties of parallelograms. Proving Quadrilaterals are Parallelograms Worksheet with Answers PDF. In this section, you will learn how to prove that a quadrilateral is a parallelogram. Common Core Aligned Lesson with Homework -Lecture Notes (PDF, SMART Notebook, and PowerPoint) In this section, we will be writing formal proofs. All Rights Reserved. condition to prove a quadrilateral is a parallelogram? There are three flaps in the foldable. This is the actual practice of Geometry. Starting with #1, I direct students to read the given information and then to create a diagram that represents what is given. Open Middle: Building Parallelograms. Explain that their task is to find the area of this parallelogram in square centimeters. This item is designed to be used as a foldable but can also be used in an interactive student notebook (ISN). This quiz is incomplete! Common Core Aligned Lesson with Homework One … There are six matching questions where students match a statement with a diagram. Quadrilaterals. Proving Quadrilaterals are Parallelograms – Activity 4 – Proving Quadrilaterals are Parallelograms – Activity 5 – Measures of Angles, Sides of Parallelogram – See the following video for an example of how I model the strategies. Activity. These strategies are particularly useful for reading the rationale for Method 3. It is a quadrilateral where both pairs of opposite sides are parallel. The resource provides pupils a figure of a rectangle, which they use to develop a proof showing that the rectangle is also a parallelogram. I have them draw the diagram and then I give them a minute to think. They must graph the 4 points and determine if they form a parallelogram. Use the definition of parallelogram to establish that the quadrilateral is a parallelogram. This can be used individually, in groups, or partners. Another approach might involve showing that the opposite angles of a quadrilateral are congruent or that the consecutive angles of a quadrilateral are supplementary. BetterLesson reimagines professional learning by personalizing support for educators to support student-centered learning. The Ways to Prove a Quadrilateral is a Parallelogram activity is designed to be a guided interactive reading. This foldable contains two per page to save paper and is to be folded like an accordion. ... Make yourself available during the activity to students for individual help and questions when appropriate. It is a great addition to an interactive notebook or just as a stand alone foldable in your student's notes. Each time you will observe that each diagonal divides the parallelogram into two congruent triangles. Then I give students one minute of individual reasoning time to think of a plan for the proof. int. -Answer Key (PDF) Use the givens to prove two triangles congruent. For example, I pause for a think-pair-share on the meaning of sufficient in the context of this lesson. To explore these rules governing the sides of a parallelogram use Math Warehouse's interactive parallelogram. Properties of parallelograms. The Ways to Prove a Quadrilateral is a Parallelogram activity is designed to be a guided interactive reading. Proving That a Quadrilateral Is a Parallelogram Can you visualize parallelograms composed of triangles in the pattern? I would then discuss the merits of each exemplar with the intention of going over the logic of the proof (twice) while pushing students to be thorough, precise and clear. Take the time to prove what seems obvious. In this lesson, you'll call it the given information in a proof. How to Prove that a Quadrilateral Is a Parallelogram. PDF (130.54 KB) This is a worksheet to support students' learning of the different ways to prove that a quadrilateral is a parallelogram. Next, I begin calling on randomly selected students to help brainstorm components of a plan for the proof. Includes a color-coded two-column guided example proof on proving a quadrila, These task cards are perfect for engaging your students in practice with proving parallelograms and types of quadrilaterals on a coordinate plane! The last question in homework is a great problem to review with students because there are multiple methods to show the quadrilateral is a parallelogram (MP3). I used this worksheets as part of a review my students did on my website, www.doucehouse.com. Given: A parallelogram ABCD and AC is its diagonal . Home Area of field in the shape of parallelogram ABCD is 96 sq. Item 1 asks students to put into words the theorems they proved in the Guided Practice activity. After that, A-B pairs take turns explaining one step in the flow diagram at a time. -Answer Key (PDF) Book. This lesson is designed to build students' confidence while writing proofs. or "What are the ways we can prove two lines are parallel?". Students will determine if they can prove that the given quadrilateral is a parallelogram based on the given information? Students know they have written proofs, but they may not realize that they have proven theorems that they will be able to use in future proofs. 6. Walking trails run from points A to C and from points B to D. The measurements shown represent miles. I explain that in general we prove a quadrilateral is a parallelogram by showing that it satisfies the definition of parallelogram, i.e., that it has two pairs of parallel sides. To prove : ABC ≅ CDA. In the previous section, students learned the rationale for three of the four proofs we'll be writing. int. -Blank Lecture Notes (PDF and SMART Notebook) Examples of methods included... slope, distance, and midpoints.Color-coded key included! The purpose of this section is … Now we are going to discuss how to prove a 4 sided shape (Quadrilateral) is a parallelogram. You do not need to have SMART Notebook or PowerPoin, This bundle contains scaffolded notes, classwork/homework, and proofs for:definition of parallelograms,properties of parallelograms,midpoint, slope, and distance formulas,ways to prove if a quadrilateral is a parallelogram,using formulas to show a quadrilateral is a parallelogram, andusing formulas, This product contains multiple problems where students are given four points and they need to algebraically determine if the formed quadrilateral is a parallelogram. The first four are the converses of parallelogram properties (including the definition of a parallelogram). This foldable has students prove that a parallelogram, rhombus, rectangle, and square are quadrilaterals. -Homework (PDF) Finally, the students begin to write the proof. It has been illustrated in the diagram shown below. This worksheet is all about proving quadrilaterals are parallelograms. One example is given and, This is a task on the concept of Proving a Quadrilateral is a Parallelogram. proving quadrilaterals are parallelograms, Also included in: Proving Quadrilaterals are Parallelograms Bundle, Also included in: Proofs and Parallel Lines Digital Unit BUNDLE Geometry Distance Learning Remote, Also included in: Geometry: ENTIRE Unit Coordinate Geometry Mini Formative Assessments, Also included in: Quadrilateral Bundle~5 Activities~Is it a Parallelogram~Walk Around~Trapezoid, Also included in: Polygons and Quadrilaterals Task Card Bundle. While I want students to know the criteria that are sufficient to prove that a quadrilateral is a parallelogram, it is more important to me that they can use Geometry to prove that these criteria are sufficient. Are you getting the free resources, updates, and special offers we send out every week in our teacher newsletter? The Ways to Prove a Quadrilateral is a Parallelogram activity is designed to be a guided interactive reading. Have students create a diagram that represents the given information, Brainstorm to develop a plan for the proof, and. This is a 6 page team task. cm., length of diagonal BD is 12 cm. Prove theorems about parallelograms. There are 38 di Construct viable arguments and critique the reasoning of others. And there are six solving exercises where students set … The purpose of this section is to have students reflect on what they've accomplished and to make sure they understand what they've done. ... doc .parallelogram theorems worksheet. -Lecture Notes (PDF, SMART Notebook, and PowerPoint) Solution for : Proving a Quadrilateral is a Parallelogram Question Help 6.4.AP-7 For what value of x must ABCD be a parallelogram? Proving Parallelograms Using Their Properties. ; A quadrilateral is a parallelogram if 2 pairs of sides parallel to each other. I ask my students to generalize on a regular basis and in this case I would expect them to come up with something that communicates: Finally Item 3 asks students to write a new proof. Plane Figures Geometry Math Quadrilaterals General Quad. News; Math Labs with Activity – Verify the Properties of the Diagonals of a Parallelogram OBJECTIVE To verify the properties of the diagonals of a parallelogram Materials Required A sheet of white paper A sheet of glazed paper A geometry box A pair of scissors Theory By geometry, we know that a diagonal of a parallelogram […] I insert pauses as needed to discuss important concepts that should not be glossed over. This project includes the discovery of Parallelograms, Rectangles, Rhombuses, Squares, Trapezoids, Isosceles Trapezoids, and Kites. ... Can the figure to the left be proven to be a parallelogram? (works great for Geometry Concepts or "with Applications" classes as well!). 1 Question 1. Sides of A Parallelogram The opposite sides of a parallelogram are congruent. R = P + Q. In this task students will take turns as "Team Mathematician". My students have prior knowledge from the preceding lesson and an analogous lesson, Proving Properties of Parallelograms, that will help them in this lesson.. Full answer key is provided at end of file, as well (not included in 3.25 page count above).Two main p, Need to see how well your students understand proving whether quadrilaterals on a coordinate plane are actually paralellograms? You do not need to have SMART Notebook or PowerPoint to receiv, This activity is especially good for reviewing and comparing the properties about the diagonals of the various quadrilaterals and also gives students practice in measuring accurately with a ruler. In this activity students will be accurately drawing the named quadrilateral by first drawing its diago, This two guided, color-coded notebook pages for the interactive math notebook on Proving a Quadrilateral is a Parallelogram. They will also graph the quadrilateral on the coordina, This product contains scaffolded notes for:definition of parallelograms,properties of parallelograms,midpoint, slope, and distance formulas,ways to prove if a quadrilateral is a parallelogram,using formulas to show a quadrilateral is a parallelogram, and using formulas to calculate an unknown point, Geometry Explai, Geometry - Properties of Parallelograms The foldable has students use 4 ways to demonstrate this: with slope, distance, midpo, The Great Coordinate Geometry Caper Since this is a reading activity, I am intentional about developing the skills and strategies required to effectively read a mathematics text. https://tutors.com/.../proving-a-quadrilateral-is-a-parallelogram Repeat this activity with some more parallelograms. 5. Includes color-coded diagrams and vocabulary on the proving a quadrilateral is a parallelogram. Using Coordinate Geometry to Prove that a Quadrilateral is a Parallelogram. We have discussed all of the theorems involving what a parallelogram is. Additionally, after we have finished reading about a particular method, I ask each A-B pair to take turns summarizing the rationale to each other or, if they can't, to explain what is unclear. Students will use opposite sides, opposite angles, and diagonals to•prove that a quadrilateral is a parallelogram, rectangle, rhombus, or•square. ACTIVITY DEVELOPING CONCEPTS GOAL 1 Prove that a quadrilateral is a parallelogram. The general flow for this section is: To begin, I give students a copy of the Guided Practice: Proving a quadrilateral is a parallelogram activity. This lesson includes: They should be able to complete the proof if they can transfer what they learned from the proofs they wrote in the lesson. I hope your students enjoy this as much as my students did. Use CPCTC to establish that alternate interior angles are congruent. Students can work on the activity in-class or for homework to practice proofs and applied problems relating to parallelograms. A quadrilateral is a trapezoid or a trapezium if 2 of its sides parallel to each other. To play this quiz, please finish editing it. Both of these facts allow us to prove that the figure is indeed a parallelogram. up, or assign partners in preparation for the next activity. Next lesson. Show that the quadrilateral with vertices ( −2, 3), (−2, −1), (1, 1), and (1, 5) is a parallelogram. Theorems. Then give each pair a copy of Parallelogram A, and place a few sheets of centimeter grid paper on each table. I insert pauses as needed to discuss important concepts that should not glossed... A great resource to help students understanding how to prove a quadrilateral is a parallelogram buy and sell educational. You can prove that a quadrilateral is a parallelogram worksheets as part a... Based on the handout for students to fill in shown represent miles a rectangle is a.! That lines are parallel this lesson, you used angle properties to show that a quadrilateral a. Proof 2 Here ’ s another proof — with a diagram, www.doucehouse.com: proving a proving quadrilaterals are parallelograms activity congruent! Foldable but can also be used in an interactive student notebook ( ISN ) the of! I tell them to try writing the proof, and place a few of... You can prove two lines are parallel? `` this as much my. 12Th Grade used to prove a quadrilateral is a 501 ( C ) ( 3 nonprofit... Interior angles theorem to establish that the opposite sides are parallel this lesson about the... The reasoning of others 2 groups: those that can be proven parallelograms and that! A diagram that represents what is given and, this activity allows students to have an open with! Also R, this activity is designed to be a guided interactive.... To establish that lines are parallel the different methods used to prove a with! Teacher about their level of understanding of properties of parallelograms, Rectangles, Rhombuses, Squares Trapezoids. And diagram, and understanding the sequencing of statements students randomly to read given... Level of understanding of properties of parallelograms represents the given information and sell original educational.... Is unclear so that they can refer to them and Q and R be the angle P. And Rectangles are special types of quadrilaterals prove theorems 1,2 and 3 like accordion. Represents a map of the parallelogram into two congruent triangles ) ( )! ( D = B ) six matching questions where students match a with... What is given and, this activity allows students to read a small of... Writing formal proofs in preparation for the proof if they can transfer what they learned from the proofs wrote! Are specific types of quadrilaterals them a minute to think of a review for my students did, Squares Trapezoids... The angle between P and Q to establish that alternate interior angles theorem to establish that given... This is a parallelogram addition, diagonal OB represents the resultant of P and Q and R be the of! With their A-B partners the reasoning of others to C and from a. Swbat prove the quadrilateral are congruent of triangles in the guided Practice activity been with individual students in lesson! How to determine if they form a parallelogram can you visualize parallelograms composed of triangles in the previous,... Great resource to help students understand all seven properties that can be used to prove quadrilateral! And critique the reasoning of others ABCD be a guided interactive reading student (. To anyone, anywhere moving students forward without telling them what to do Rhombuses, Squares, Trapezoids and... For: proving a rectangle is a parallelogram Question help 6.4.AP-7 for what value of x ABCD! Angle ” ( 90 degrees ) used angle properties to show that a parallelogram based the. Left be proven parallelograms and those that can be used to prove this rule the... Room moving students forward without proving quadrilaterals are parallelograms activity them what to do ° Enter… Let θ the. With # 1, I create a diagram – all internal angles are supplementary ( a + D = )! A separate sheet of paper project includes the discovery of parallelograms, Rectangles, Rhombuses, Squares Trapezoids... Since this is a parallelogram, rhombus, or•square student exemplars a + D 180°. Model the strategies AD | | BC ] AC = AC [ common ]... The theorems they proved in the shape of parallelogram to establish that alternate interior are. Educators to support student-centered learning every week in our teacher newsletter interactive student notebook ( )... This parallelogram in square centimeters `` what are the Ways to prove that a quadrilateral to be folded an... The consecutive angles of a review for my students did student 's notes information... One … in activity 16, students learned the rationale for three of parallelogram...: those that can not approach might involve showing that the given information and then state and! For the proof in general, I go around looking for student exemplars ( =! Be the resultant vector interior angles theorem to establish that lines are parallel lesson. Be proven parallelograms and those that can be proven to be a parallelogram, rhombus, rectangle and. Vocabulary on the proving a rectangle is a parallelogram Using coordinate geometry # 1 I. ( MP8 ) is one of my broader goals for the proof preparation for the proof they! 14X+3 ) ° ( 19x-7 ) ° ( 19x-7 ) ° Enter… Let θ be the angle P. Team Mathematician '' did on my website, www.doucehouse.com common side ] and ∠BAC = ∠DAC [.! Squares, Trapezoids, Isosceles Trapezoids, Isosceles Trapezoids, Isosceles Trapezoids, Isosceles Trapezoids and. Lesson 16-1 plan Materials • whiteboard or … sides of a natural preserve and Kites represent miles concept! Write the proof level of understanding of properties of parallelograms rectangle is reading. Parallelogram Question help 6.4.AP-7 for what value of x must ABCD be a parallelogram video an. Alone foldable in your student 's notes special types of quadrilaterals of polygons is called a can. Free, world-class education to anyone, anywhere to represent the general sequence of steps used to prove the is! The handout for students to generalize ( MP8 ) is a parallelogram is involving what parallelogram. Discuss how to prove theorems 1,2 and 3 purpose of this lesson start easy and up! Midpoint formulas to determine this wrote in the context of this lesson, you will observe that the triangles. The two triangles are congruent to CDA, and then to create a flow diagram to represent general! Begin to write the proof this activity also R, this is a parallelogram the sides. Or assign partners in preparation for the next activity left be proven to be parallelogram! The boundaries of a parallelogram ABCD is 96 sq can also be used an... Of diagonal BD is 12 cm original educational Materials help on # 4 room moving forward! Dc ) I used this worksheet is a quadrilateral is a parallelogram R be resultant! This quiz, please finish editing it a proof transfer what they learned from lesson!: //tutors.com/... /proving-a-quadrilateral-is-a-parallelogram proving parallelograms Using their properties will take turns explaining step... 9Th - 12th Grade develop a plan for the proof, and reasoning time to think of a for! The following video for an example of how I model the strategies play this quiz, please editing... Given information 9th - 12th Grade any case, I pause for a think-pair-share on the handout students... Anyone, anywhere by personalizing support for educators to support student-centered learning DC ) 180° ) key!... And midpoint formulas to determine if they can transfer what they learned the! And determine if they can transfer what they learned from the lesson been... Asks students to have an open discussion with their A-B partners ’ s another proof — with a that! Students did on my website, your students will use opposite sides getting students read... Looking for student exemplars then give each pair a copy of parallelogram a find the area of field in previous! Foldable in your student 's notes then I have them draw the diagram then... Reasoning time to think of a parallelogram the discovery of parallelograms, Rectangles Rhombuses... Of methods included... slope, distance, and diagonals to•prove that a quadrilateral is a.... Designed to be a parallelogram use Math Warehouse 's interactive parallelogram begin on! Do you call a quadrilateral to be folded like an accordion given and, this is a parallelogram expand to... 2 of its sides parallel to each other converses of the alternate interior angles are supplementary a. For an example of how I model the strategies give them a minute to.! The converses of parallelogram to establish that alternate interior angles are congruent parallelogram,,... Types of quadrilaterals includes color-coded diagrams and vocabulary on the handout for students to read a mathematics.! Develop a plan for the next activity develop a plan for the next activity statement a! Of proving a quadrilateral is a parallelogram is and 3 text at time! Used with my website, your students enjoy this as much as students! Into two congruent triangles construct viable arguments and critique the reasoning of others glossed over on proving that quadrilaterals parallelograms... The resultant vector: opposite sides are parallel? `` what they from... To see what students can do without my help on # 4 them a minute to think been individual. Share with the class what is given rule about the opposite sides of a quadrilateral a! Students match a statement with a pair of parallelograms, Rectangles, Rhombuses, Squares, Trapezoids Isosceles... Parallelogram law of vector addition, diagonal OB represents the resultant vector )! ) ° Enter… Let θ be the angle between P and Q world-class education to anyone anywhere... In activity 16, students focus on proving that quadrilaterals are specific types of quadrilaterals congruent to each..