Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems. Proving quadrilaterals are parallelograms each pair of hinges are opposite sides of a quadrilateral. Square, rectangle, rhombus, kite, trapezoid, and parallelogram. The files listed below are the power point note presentations. I explain that well be writing four proofs that quadrilaterals are parallelograms and that these four proofs will differ only in terms of the information that is given. Mcgraw geometry parallelograms free pdf file sharing. When these documents are converted to the portable document format pdf, the embedded objects can be retained using the microsoft word 2007 pdf and xps addin.
This worksheet is all about proving quadrilaterals are parallelograms. Jump to the end of the proof and ask yourself whether you could prove that qrvu is a parallelogram if you knew that the triangles were congruent. You can prove that it is a parallelogram by showing that it has two pairs of parallel sides. Proving that quadrilaterals are parallelograms worksheet. Proving that a quadrilateral is a parallelogram video. I explain that in general we prove a quadrilateral is a parallelogram by showing that it satisfies the definition of parallelogram. There are also theorems that allow us to use other properties of quadrilaterals to conclude that it is a parallelogram. If a quadrilateral is a parallelogram, then its consecutive angles are supplementary. Geometry geometry proofs, quadrilaterals, parallograms.
The activity illustrates one way to prove that a quadrilateral is a parallelogram. The definition of a parallelogram gives one way to prove that a quadrilateral is a parallelogram show both pair of opposite sides are parallel. Use coordinate geometry to prove the quadrilateral is a parallelogram. Identifying and verifying parallelograms given a parallelogram, you can use the parallelogram opposite sides theorem. Dont forget to label also, if a given piece of information is that we have a quadrilateral it does not mean we have any parallelogram.
A paragraphstyle proof of this theorem is given below. Proving that a quadrilateral is a parallelogram betterlesson. I explain that in general we prove a quadrilateral is a parallelogram by showing that it satisfies the definition of parallelogram, i. Jul 07, 2018 mar 31, 2015 additional documents, spreadsheets or multimedia items may be embedded into microsoft office word documents. Proving quadrilaterals in the coordinate plane mathematical goals prove theorems pertaining to lines and angles. Parallelograms quadrilaterals are foursided polygons parallelogram. Proving quadrilaterals are parallelograms goals p prove that a quadrilateral is a parallelogram. A is a quadrilateral with both pairs of opposite sides parallel. Geometry chapter 7, section 3 notes proving that a quadrilateral is a parallelogram. Properties of parallelograms and special parallelograms. This is a foldable to help students organize the ways to prove a quadrilateral is a parallelogram using coordinate geometry. To use relationships to prove quadrilaterals are parallelograms.
This geometry worksheet contains problems on proving if certain quadrilaterals are parallelograms and requires an understanding of the different theorems and properties required to prove that a quadrilateral is a parallelogram. Proving quadrilaterals are parallelograms wyzant resources. Show two sides of the triangle are perpendicular by demonstrating their slopes are. Any one of the following methods might be used to prove that a quadrilateral is a parallelogram. This packet is on traversals leading into proving parallelograms. Proving quadrilaterals are parallelograms pdf eooqtie.
Trapezoids are quadrilaterals with exactly one pair of opposite parallel lines. Parallelograms proving a quadrilateral is a parallelogram. Big idea two pairshare proofs await to challenge students in this lesson on proving that quadrilaterals are parallelograms. Four theorems to prove quadrilaterals are parallelograms view. Mar 06, 20 this video shows you the four ways to prove a quadrilateral is a parallelogram. The packet also has a summary of reasons that student should know up to this point. Depending on what information you have to work with, youll be.
Most of the work we did was computationbased because we were already given the fact that the figures were parallelograms. Using cpctc corresponding parts of congruent triangles are congruent, you could show that qrvu has two pairs of congruent sides, and that would make it a parallelogram. A quadrilateral is a parallelogram iff the diagonals bisect each other. Proving quadrilaterals worksheets lesson worksheets. Choose from 255 different sets of proving parallelograms flashcards on quizlet. Prove triangles congruent using special parallelogram properties pages 1823 hw.
If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram. Day 2 ways to prove a quadrilateral is a parallelogram warm. In the previous section, we learned about several properties that distinguish parallelograms from other quadrilaterals. I start easy and work up to more challenging problems. Swbat prove that quadrilaterals are parallelograms using the definition of parallelogram and six key parallelogram property theorems. By theorem 634, the quadrilateral is a parallelogram. What is the sum of the degrees of the interior angles of a 19gon. Proving a quadrilateral is a parallelogram worksheets. A quadrilateral is a parallelogram iff both pairs of its opposite angles are congruent. If both pairs of opposite sides are congruent, then the quadrilateral is a parallelogram. Proving a quadrilateral a parallelogram geometry proof how to help duration.
Proving that a quadrilateral is a parallelogram any of the methods may be used to prove that a quadrilateral is a parallelogram. Applying conditions for parallelograms determine if the quadrilateral must be a parallelogram. Worksheets are quadrilateral proofs packet 2, geometry work quadrilaterals, proofs of quadrilateral properties, name geometry proving that a quadrilateral is a, polygons quadrilaterals and special parallelograms, proving a quadrilateral is a rhombus rectangle or a, geometry honors coordinate geometry proofs, geometry coordinate geometry proofs. There are 6 methods of proving that a figure is a parallelogram. The lines in a trapezoid that are parallel are called the bases, and the lines that are not parallel are called the legs. Learn vocabulary, terms, and more with flashcards, games, and other study tools.
Determine the sum of both the interior and exterior angle measures of a polygon. Proving parallelograms assignment determine whether each of the following quadrilaterals are parallelograms. Complete the following theorems which provide four more ways. Nov 17, 2010 geometry notes proving quadrilateral are parallelograms. It is a great addition to an interactive notebook or just as a stand alone foldable in your students notes. Other results for 8 2 study guide and intervention parallelograms answer key. Show that a quadrilateral is a parallelogram in the coordinate plane. This makes the quadrilateral a parallelogram and a rectangle.
If one pair of oppos ite sides of a quadrilateral is congruent and parallel. If an angle is supplementary to both consecutive angles 6. How to prove that quadrilateral is a parallelogram quora. Proving properties of special quadrilaterals adapted from walch education. Because opposite sides of the quadrilateral are congruent, it is a parallelogram. Parallelogram rhombus rectangle square trapezoid isosceles trapezoid three parts formulate a plan use slope, midpoint, andor distance formulas to execute plan create concluding statement to justify the proof 5 example. Name geometry proving that a quadrilateral is a parallelogram any. Any of the methods may be used to prove that a quadrilateral is a parallelogram. When you mark diagrams of quadrilaterals, use matching arrowheads to indicate which sides are.
Proving that a quadrilateral is a parallelogram using. Lecture notes pdf, smart notebook, and powerpoint blank lecture notes pdf and smart notebook homework pdf answer key pdf you do not need to have smart notebook or powerpoint to receive the full benefits of this product. If in a quadrilateral, each pair of opposite angles are. Proving quadrilaterals are parallelograms worksheets. Practice finding the areaofsquares, rectanglesandparallelogramsworksheet has 10 great questions to assess if your students have mastered applying the formulas to calculate the area of a square, rectangle, and parallelogram. Apart from cyclic quadrilaterals, these special quadrilaterals and their properties have been. Prove triangles congruent using trapezoids pages 26 30 hw.
Students are then asked to determine whether given quadrilaterals are parallelograms based on these concepts, as well as solve problems related to these concepts using algebra. Rectangle a rectangle has four sides and four right angles. Students will identify and use tests to prove quadrilaterals are parallelograms. Recognize the conditions that ensure a quadrilateral is a parallelogram. Prove quadrilaterals are parallelograms lesson with. Theorem 83 stated that the opposite sides of a parallelogram are congruent. Suppose you are given a quadrilateral and believe that it is a parallelogram.
Summary properties of parallelograms definition of parallelogram, p. Day 2 ways to prove a quadrilateral is a parallelogram. Jrn of the interior angles of a polygon is 18000, how many cnz. In this video i will introduce 5 ways to prove a quadrilateral is a parallelogram and then go through two such proofs as examples. Trapezoids are not parallelograms because they do not have two pairs of opposite lines that are parallel. The 73angle is supplementary to both its corresponding angles. This module will deal with two of them parallelograms and rectangles leaving rhombuses, kites, squares, trapezia and cyclic quadrilaterals to the module, rhombuses, kites, and trapezia. Learn proving parallelograms with free interactive flashcards. We can prove a quadrilateral to be a parallelogram, if we prove any of the properties given below if each pair of opposite sides of a quadrilateral are equal then it is a parallelogram. A rectangle is a parallelogram, so opposite sides are parallel.
A quadrilateral is a parallelogram but first, lets go over five ways you can use to prove that a quadrilateral is a parallelogram. Start studying 5 ways to prove a quadrilateral is a parallelogram. Geometry notes proving quadrilateral are parallelograms by g. If a quadrilateral is a parallelogram, then its opposite angles are congruent. Geo 63 proving that a quadrilateral is a parallelograms1. Shortcuts to proving quadrilaterals are parallelograms. Parallelograms and rectangles 4 a guide for teachers assumed knowledge introductory plane geometry involving points and lines, parallel lines and transversals, angle sums of triangles and quadrilaterals, and general angle. Describe, classify, and explain relationships among the quadrilaterals square, rectangle, rhombus, parallelogram, trapezoid, and kite. A 8 gmtaldie g 4wwijt uhf ximnef uijn pint 0e2 yg gexo6m5ewtkr0y x. Proving parallelograms properties of a parallelogram. Geometry lesson 62 properties of parallelograms answers.