DOCSLIB.ORG

1. Saying That "Diagonals Bisect Each Other" Is Enough to Conclude That a Given Quadrilateral Is a ______

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
1. Saying That 1. Saying that "diagonals bisect each other" is enough to conclude that a given quadrilateral is a ____________________. a) parallelogram b) isosceles trapezoid c) kite d) rhombus e) rectangle f) square 2. A square is __________________ a rhombus. a) always b) sometimes c) never 3. Diagonals of a trapezoid are ___________________congruent. a) always b) sometimes c) never 4. There is exactly one pair of opposite congruent sides in: (Choose all that apply or one of the last two choices.) a) a kite b) a parallelogram c) a trapezoid d) a rhombus e) a rectangle f) an isosceles trapezoid g) a square h) any quadrilateral i) none of the above 1 5. A rhombus is _________________ a square: a) always b) sometimes c) never 6. A trapezoid is _________________ a parallelogram: a) always b) sometimes c) never 7. Both pairs of opposite angles are congruent in: (Choose all that apply or one of the last two choices.) a) a kite b) a parallelogram c) a trapezoid d) a rhombus e) a rectangle f) an isosceles trapezoid g) a square h) any quadrilateral i) none of the above 8. Diagonals of a trapezoid ________________ bisect each other. a) always b) sometimes c) never 9. Base angles of a trapezoid are _______________congruent. a) always b) sometimes c) never 2 10. There could be exactly two right angles in: (Choose all that apply or one of the last two choices.) a) a kite b) a parallelogram c) a trapezoid d) a rhombus e) a rectangle f) an isosceles trapezoid g) a square h) any quadrilateral i) none of the above 11. Saying that "all angles are congruent" is enough to conclude that a given quadrilateral is a ___________________. a) parallelogram b) isosceles trapezoid c) kite d) rhombus e) rectangle f) square 12. There is exactly one pair of opposite congruent angles in: (Choose all that apply or one of the last two choices.) a) a kite b) a parallelogram c) a trapezoid d) a rhombus e) a rectangle f) an isosceles trapezoid g) a square h) any quadrilateral i) none of the above 13. A rhombus is ______________ a parallelogram. a) always b) sometimes c) never 3 14. A square is ______________________ a parallelogram. a) always b) sometimes c) never 15. A square is __________________ a rectangle. a) always b) sometimes c) never 16. Saying that "consecutive angles are supplementary" is enough to conclude that a given quadrilateral is a ______________________. a) parallelogram b) isosceles trapezoid c) kite d) rhombus e) rectangle f) square 17. Diagonals of an isosceles trapezoid are _______________ congruent. a) always b) sometimes c) never 4 18. Diagonals are always perpendicular in: (Choose all that apply or one of the last two choices.) a) a kite b) a parallelogram c) a trapezoid d) a rhombus e) a rectangle f) an isosceles trapezoid g) a square h) any quadrilateral i) none of the above 19. Diagonals always bisect each other in: (Choose all that apply or one of the last two choices.) a) a kite b) a parallelogram c) a trapezoid d) a rhombus e) a rectangle f) an isosceles trapezoid g) a square h) any quadrilateral i) none of the above 20. Saying that "diagonals bisect each other" is enough to conclude that a given quadrilateral is a _____________________. a) parallelogram b) isosceles trapezoid c) kite d) rhombus e) rectangle f) square 5 21. Base angles of an isosceles trapezoid are _________________congruent. a) always b) sometimes c) never 22. A kite is _________________ a rhombus. a) always b) sometimes c) never 23. A parallelogram is ___________________ a trapezoid. a) always b) sometimes c) never 24. Diagonals always bisect BOTH pairs of opposite angles in: a) a kite b) a parallelogram c) a trapezoid d) a rhombus e) a rectangle f) an isosceles trapezoid g) a square h) any quadrilateral i) none of the above 6 25. Diagonals are congruent in: a) a kite b) a parallelogram c) a trapezoid d) a rhombus e) a rectangle f) an isosceles trapezoid g) a square h) any quadrilateral i) none of the above 26. Saying that "diagonals are perpendicular and congruent" is enough to conclude that a given quadrilateral is a _____________________. a) parallelogram b) isosceles trapezoid c) kite d) rhombus e) rectangle f) square 27. Saying that "diagonals are perpendicular and opposite sides are parallel" is enough to conclude that a given quadrilateral is a __________________. a) parallelogram b) isosceles trapezoid c) kite d) rhombus e) rectangle f) square 28. Non­parallel sides of an isosceles trapezoid are ________________ congruent. a) always b) sometimes c) never 29. Saying that "diagonals are congruent and opposite sides are parallel" is enough to conclude that a given quadrilateral is a ______________________. a) parallelogram b) isosceles trapezoid c) kite d) rhombus e) rectangle f) square 7 30. A trapezoid is _______________ a parallelogram. a) always b) sometimes c) never 31. Bases of a trapezoid are _______________ congruent. a) always b) sometimes c) never 8.
Load more

Recommended publications
  • Quadrilateral Theorems
    Quadrilateral Theorems Properties of Quadrilaterals: If a quadrilateral is a TRAPEZOID then, 1. at least one pair of opposite sides are parallel(bases) If a quadrilateral is an ISOSCELES TRAPEZOID then, 1. At least one pair of opposite sides are parallel (bases) 2. the non-parallel sides are congruent 3. both pairs of base angles are congruent 4. diagonals are congruent If a quadrilateral is a PARALLELOGRAM then, 1. opposite sides are congruent 2. opposite sides are parallel 3. opposite angles are congruent 4. consecutive angles are supplementary 5. the diagonals bisect each other If a quadrilateral is a RECTANGLE then, 1. All properties of Parallelogram PLUS 2. All the angles are right angles 3. The diagonals are congruent If a quadrilateral is a RHOMBUS then, 1. All properties of Parallelogram PLUS 2. the diagonals bisect the vertices 3. the diagonals are perpendicular to each other 4. all four sides are congruent If a quadrilateral is a SQUARE then, 1. All properties of Parallelogram PLUS 2. All properties of Rhombus PLUS 3. All properties of Rectangle Proving a Trapezoid: If a QUADRILATERAL has at least one pair of parallel sides, then it is a trapezoid. Proving an Isosceles Trapezoid: 1st prove it’s a TRAPEZOID If a TRAPEZOID has ____(insert choice from below) ______then it is an isosceles trapezoid. 1. congruent non-parallel sides 2. congruent diagonals 3. congruent base angles Proving a Parallelogram: If a quadrilateral has ____(insert choice from below) ______then it is a parallelogram. 1. both pairs of opposite sides parallel 2. both pairs of opposite sides ≅ 3.
    [Show full text]
  • Properties of Equidiagonal Quadrilaterals (2014)
    Forum Geometricorum Volume 14 (2014) 129–144. FORUM GEOM ISSN 1534-1178 Properties of Equidiagonal Quadrilaterals Martin Josefsson Abstract. We prove eight necessary and sufficient conditions for a convex quadri- lateral to have congruent diagonals, and one dual connection between equidiag- onal and orthodiagonal quadrilaterals. Quadrilaterals with both congruent and perpendicular diagonals are also discussed, including a proposal for what they may be called and how to calculate their area in several ways. Finally we derive a cubic equation for calculating the lengths of the congruent diagonals. 1. Introduction One class of quadrilaterals that have received little interest in the geometrical literature are the equidiagonal quadrilaterals. They are defined to be quadrilat- erals with congruent diagonals. Three well known special cases of them are the isosceles trapezoid, the rectangle and the square, but there are other as well. Fur- thermore, there exists many equidiagonal quadrilaterals that besides congruent di- agonals have no special properties. Take any convex quadrilateral ABCD and move the vertex D along the line BD into a position D such that AC = BD. Then ABCD is an equidiagonal quadrilateral (see Figure 1). C D D A B Figure 1. An equidiagonal quadrilateral ABCD Before we begin to study equidiagonal quadrilaterals, let us define our notations. In a convex quadrilateral ABCD, the sides are labeled a = AB, b = BC, c = CD and d = DA, and the diagonals are p = AC and q = BD. We use θ for the angle between the diagonals. The line segments connecting the midpoints of opposite sides of a quadrilateral are called the bimedians and are denoted m and n, where m connects the midpoints of the sides a and c.
    [Show full text]
  • Midsegment of a Trapezoid Parallelogram
    Vocabulary Flash Cards base angles of a trapezoid bases of a trapezoid Chapter 7 (p. 402) Chapter 7 (p. 402) diagonal equiangular polygon Chapter 7 (p. 364) Chapter 7 (p. 365) equilateral polygon isosceles trapezoid Chapter 7 (p. 365) Chapter 7 (p. 402) kite legs of a trapezoid Chapter 7 (p. 405) Chapter 7 (p. 402) Copyright © Big Ideas Learning, LLC Big Ideas Math Geometry All rights reserved. Vocabulary Flash Cards The parallel sides of a trapezoid Either pair of consecutive angles whose common side is a base of a trapezoid A polygon in which all angles are congruent A segment that joins two nonconsecutive vertices of a polygon A trapezoid with congruent legs A polygon in which all sides are congruent The nonparallel sides of a trapezoid A quadrilateral that has two pairs of consecutive congruent sides, but opposite sides are not congruent Copyright © Big Ideas Learning, LLC Big Ideas Math Geometry All rights reserved. Vocabulary Flash Cards midsegment of a trapezoid parallelogram Chapter 7 (p. 404) Chapter 7 (p. 372) rectangle regular polygon Chapter 7 (p. 392) Chapter 7 (p. 365) rhombus square Chapter 7 (p. 392) Chapter 7 (p. 392) trapezoid Chapter 7 (p. 402) Copyright © Big Ideas Learning, LLC Big Ideas Math Geometry All rights reserved. Vocabulary Flash Cards A quadrilateral with both pairs of opposite sides The segment that connects the midpoints of the parallel legs of a trapezoid PQRS A convex polygon that is both equilateral and A parallelogram with four right angles equiangular A parallelogram with four congruent sides and four A parallelogram with four congruent sides right angles A quadrilateral with exactly one pair of parallel sides Copyright © Big Ideas Learning, LLC Big Ideas Math Geometry All rights reserved.
    [Show full text]
  • Cyclic Quadrilaterals
    GI_PAGES19-42 3/13/03 7:02 PM Page 1 Cyclic Quadrilaterals Definition: Cyclic quadrilateral—a quadrilateral inscribed in a circle (Figure 1). Construct and Investigate: 1. Construct a circle on the Voyage™ 200 with Cabri screen, and label its center O. Using the Polygon tool, construct quadrilateral ABCD where A, B, C, and D are on circle O. By the definition given Figure 1 above, ABCD is a cyclic quadrilateral (Figure 1). Cyclic quadrilaterals have many interesting and surprising properties. Use the Voyage 200 with Cabri tools to investigate the properties of cyclic quadrilateral ABCD. See whether you can discover several relationships that appear to be true regardless of the size of the circle or the location of A, B, C, and D on the circle. 2. Measure the lengths of the sides and diagonals of quadrilateral ABCD. See whether you can discover a relationship that is always true of these six measurements for all cyclic quadrilaterals. This relationship has been known for 1800 years and is called Ptolemy’s Theorem after Alexandrian mathematician Claudius Ptolemaeus (A.D. 85 to 165). 3. Determine which quadrilaterals from the quadrilateral hierarchy can be cyclic quadrilaterals (Figure 2). 4. Over 1300 years ago, the Hindu mathematician Brahmagupta discovered that the area of a cyclic Figure 2 quadrilateral can be determined by the formula: A = (s – a)(s – b)(s – c)(s – d) where a, b, c, and d are the lengths of the sides of the a + b + c + d quadrilateral and s is the semiperimeter given by s = 2 . Using cyclic quadrilaterals, verify these relationships.
    [Show full text]
  • Cyclic and Bicentric Quadrilaterals G
    Cyclic and Bicentric Quadrilaterals G. T. Springer Email: [email protected] Hewlett-Packard Calculators and Educational Software Abstract. In this hands-on workshop, participants will use the HP Prime graphing calculator and its dynamic geometry app to explore some of the many properties of cyclic and bicentric quadrilaterals. The workshop will start with a brief introduction to the HP Prime and an overview of its features to get novice participants oriented. Participants will then use ready-to-hand constructions of cyclic and bicentric quadrilaterals to explore. Part 1: Cyclic Quadrilaterals The instructor will send you an HP Prime app called CyclicQuad for this part of the activity. A cyclic quadrilateral is a convex quadrilateral that has a circumscribed circle. 1. Press ! to open the App Library and select the CyclicQuad app. The construction consists DEGH, a cyclic quadrilateral circumscribed by circle A. 2. Tap and drag any of the points D, E, G, or H to change the quadrilateral. Which of the following can DEGH never be? • Square • Rhombus (non-square) • Rectangle (non-square) • Parallelogram (non-rhombus) • Isosceles trapezoid • Kite Just move the points of the quadrilateral around enough to convince yourself for each one. Notice HDE and HE are both inscribed angles that subtend the entirety of the circle; ≮ ≮ likewise with DHG and DEG. This leads us to a defining characteristic of cyclic ≮ ≮ quadrilaterals. Make a conjecture. A quadrilateral is cyclic if and only if… 3. Make DEGH into a kite, similar to that shown to the right. Tap segment HE and press E to select it. Now use U and D to move the diagonal vertically.
    [Show full text]
  • Rhombus Rectangle Square Trapezoid Kite NOTES
    Geometry Notes G.9 Rhombus, Rectangle, Square, Trapezoid, Kite Mrs. Grieser Name: _________________________________________ Date: _________________ Block: _______ Rhombuses, Rectangles, Squares The Venn diagram below describes the relationship between different kinds of parallelograms: A rhombus is a parallelogram with four congruent sides A rectangle is a parallelogram with four right angles A square is a parallelogram with four congruent sides and four right angles Corollaries: A quadrilateral is a rhombus IFF it has four congruent sides A quadrilateral is a rectangles IFF it has four right angles A quadrilateral is a square IFF it is a rhombus and a rectangle. Since rhombuses, squares, and rectangles are parallelograms, they have all the properties of parallelograms (opposite sides parallel, opposite angles congruent, diagonals bisect each other, etc.) In addition… Rhombus Rectangle Square 4 congruent sides 4 right angles 4 congruent sides diagonals bisect angles diagonals congruent diagonals bisect each other diagonals perpendicular diagonals perpendicular 4 right angles diagonals congruent Theorems: A parallelogram is a rhombus IFF its diagonals are perpendicular. A parallelogram is a rhombus IFF each diagonal bisects a pair of opposite angles. A parallelogram is a rectangle IFF its diagonals are congruent. Examples: 1) Given rhombus DEFG, are the statements 2) Classify the parallelogram and find missing sometimes, always, or never true: values: a) b) a) D F b) D E c) DG GF 3) Given rhombus WXYZ 4) Given rectangle PQRS and and mXZY 34, find: mRPS 62 and QS=18, a) mWZV b) WY c) XY find: a) mQPR b) mPTQ c) ST Geometry Notes G.9 Rhombus, Rectangle, Square, Trapezoid, Kite Mrs.
    [Show full text]
  • Two-Dimensional Figures a Plane Is a Flat Surface That Extends Infinitely in All Directions
    NAME CLASS DATE Two-Dimensional Figures A plane is a flat surface that extends infinitely in all directions. A parallelogram like the one below is often used to model a plane, but remember that a plane—unlike a parallelogram—has no boundaries or sides. A plane figure or two-dimensional figure is a figure that lies completely in one plane. When you draw, either by hand or with a computer program, you draw two-dimensional figures. Blueprints are two-dimensional models of real-life objects. Polygons are closed, two-dimensional figures formed by three or more line segments that intersect only at their endpoints. These figures are polygons. These figures are not polygons. This is not a polygon A heart is not a polygon A circle is not a polygon because it is an open because it is has curves. because it is made of figure. a curve. Polygons are named by the number of sides and angles they have. A polygon always has the same number of sides as angles. Listed on the next page are the most common polygons. Each of the polygons shown is a regular polygon. All the angles of a regular polygon have the same measure and all the sides are the same length. SpringBoard® Course 1 Math Skills Workshop 89 Unit 5 • Getting Ready Practice MSW_C1_SE.indb 89 20/07/19 1:05 PM Two-Dimensional Figures (continued) Triangle Quadrilateral Pentagon Hexagon 3 sides; 3 angles 4 sides; 4 angles 5 sides; 5 angles 6 sides; 6 angles Heptagon Octagon Nonagon Decagon 7 sides; 7 angles 8 sides; 8 angles 9 sides; 9 angles 10 sides; 10 angles EXAMPLE A Classify the polygon.
    [Show full text]
  • Hexagon Fractions
    Hexagon Fractions A hexagon can be divided up into several equal, different-sized parts. For example, if we draw a line across the center, like this: We have separated the hexagon into two equal-sized parts. Each one is one-half of the hexagon. We could draw the lines differently: Here we have separated the hexagon into three equal-sized parts. Each one of these is one-third of the hexagon. 1 Another way of separating the hexagon into equal-sized parts looks like this: There are six equal-sized parts here, so each one is one-sixth of the hexagon. Each of these shapes has a special name. The shape that is one- half of the hexagon is called a trapezoid: The one that is one-third of the hexagon is a rhombus: 2 and the one that is one-sixth of the hexagon is a … Yes, a triangle! You knew that one, for sure. We can use these shapes to get an understanding of how fractions are added and subtracted. Remember that the numerator of a fraction is just a regular number. The denominator of a fraction is more than just a number, it is sort of a “thing,” like apple, dog, or flower. But it is a “numerical thing” and has a name. We should think of “half” or “third” or “tenth” or whatever as a name, just like “apple” or “dog” or “flower” is the name of something. The numerator in a fraction tells us how many of the denominators we have. For example, because the rhombus is one-third of a hexagon, we can think of the fraction “one-third” as “one rhombus.” For a hexagon, “third” and “rhombus” are two names for the same thing.
    [Show full text]
  • The Quad Squad Conjectures About Quadrilaterals
    2 The Quad Squad Conjectures About Quadrilaterals Warm Up Learning Goals Classify each figure using as • Use diagonals to draw quadrilaterals. many names as possible. • Make conjectures about the diagonals of 1. special quadrilaterals. • Make conjectures about the angle relationships of special quadrilaterals. • Categorize quadrilaterals based upon their properties. • Make conjectures about the midsegments 2. of quadrilaterals. • Understand that the vertices of cyclic quadrilaterals lie on the same circle. 3. Key Terms • coincident • isosceles trapezoid • interior angle of a • midsegment © Carnegie Learning, Inc. 4. polygon • cyclic quadrilateral • kite You have classifi ed quadrilaterals by their side measurements and side relationships. What conjectures can you make about diff erent properties of quadrilaterals? LESSON 2: The Quad Squad • M1-127 GGEO_SE_M01_T02_L02.inddEO_SE_M01_T02_L02.indd 112727 55/22/18/22/18 112:512:51 PPMM GETTING STARTED Cattywampus A quadrilateral may be convex or concave. The quadrilaterals you are most familiar with—trapezoids, parallelograms, rectangles, rhombi, and squares—are convex. For a polygon to be convex it contains all of the line segments connecting any pair of points. It is concave if and only if at least Think one pair of its interior angles is greater than 180°. about: Consider the two quadrilaterals shown. A quadrilateral has exactly two diagonals. Why can a concave quadrilateral have Convex Concave only one angle greater than 180°? 1. Draw the diagonals in the two quadrilaterals shown. What do you notice? 2. Make a conjecture about the diagonals of a convex quadrilateral and about the diagonals of a concave quadrilateral. The diagonals of any convex quadrilateral create two pairs of vertical angles © Carnegie Learning, Inc.
    [Show full text]
  • Properties of Special Parallelograms
    Project AMP Dr. Antonio Quesada – Director, Project AMP Properties of Special Parallelograms Lab Summary: This lab consists of four activities that lead students through the construction of a trapezoid. Students then explore the shapes, making conclusions about the angles, diagonals, and sides of the shapes. Key Words: trapezoid Background Knowledge: Students should be familiar with the basic geometry software commands. This lab does not provided step by step instructions for constructing a trapezoid. Therefore, students should understand that to construct a trapezoid, parallel lines must be constructed first to serve as the bases of a trapezoid. To construct the legs, students then must construct segments connecting the parallel lines. Learning Objectives: Students will identify the basic properties of trapezoids. Materials: Geometry software Suggested procedure: Split students into groups of two or three. Pass out worksheets Assessment: Check the completed worksheets and student constructions. Project AMP Dr. Antonio Quesada – Director, Project AMP Trapezoids Team members’ names: __________________________________________________ File name: ____________________________________________________________ Goal: Construct a trapezoid and analyze some of it properties. 1. This lab does not give you step by step instructions. Using your prior Cabri skills, construct a Trapezoid. The guidelines for a trapezoid are given below. A trapezoid has the following properties: · It is four sided · Two sides are parallel · Label the vertices K, L, M,
    [Show full text]
  • CAIU Polygons and Quadrilaterals
    CK-12 FOUNDATION CAIU Polygons and Quadrilaterals Hankes CK-12 Foundation is a non-profit organization with a mission to reduce the cost of textbook materials for the K-12 market both in the U.S. and worldwide. Using an open-content, web-based collaborative model termed the “FlexBook,” CK-12 intends to pioneer the generation and distribution of high-quality educational content that will serve both as core text as well as provide an adaptive environment for learning, powered through the FlexBook Platform™. Copyright © 2011 CK-12 Foundation, www.ck12.org Except as otherwise noted, all CK-12 Content (including CK-12 Curriculum Material) is made available to Users in accordance with the Creative Commons Attribution/Non-Commercial/Share Alike 3.0 Un- ported (CC-by-NC-SA) License (http://creativecommons.org/licenses/by-nc-sa/3.0/), as amended and updated by Creative Commons from time to time (the “CC License”), which is incorporated herein by this reference. Specific details can be found at http://www.ck12.org/terms. Printed: May 12, 2011 Author Wendy Hankes i www.ck12.org Contents 1 Angles in Polygons 1 1.1 Angles in Polygons ......................................... 1 2 Properties of Parallelograms 10 2.1 Properties of Parallelograms .................................... 10 3 Proving Quadrilaterals are Parallelograms 19 3.1 Proving Quadrilaterals are Parallelograms ............................ 19 4 Rectangles, Rhombuses 29 4.1 Rectangles, Rhombuses and Squares ............................... 29 5 Trapezoids and Kites 39 5.1 Trapezoids and Kites ........................................ 39 6 Quadrilaterals Review 53 6.1 Chapter 6 Review ......................................... 53 www.ck12.org ii Chapter 1 Angles in Polygons 1.1 Angles in Polygons Learning Objectives • Extend the concept of interior and exterior angles from triangles to convex polygons.
    [Show full text]
  • Area and Perimeter of Trapezoids
    Area and Perimeter of Trapezoids Bill Zahner Lori Jordan Say Thanks to the Authors Click http://www.ck12.org/saythanks (No sign in required) AUTHORS Bill Zahner To access a customizable version of this book, as well as other Lori Jordan interactive content, visit www.ck12.org CK-12 Foundation is a non-profit organization with a mission to reduce the cost of textbook materials for the K-12 market both in the U.S. and worldwide. Using an open-content, web-based collaborative model termed the FlexBook®, CK-12 intends to pioneer the generation and distribution of high-quality educational content that will serve both as core text as well as provide an adaptive environment for learning, powered through the FlexBook Platform®. Copyright © 2013 CK-12 Foundation, www.ck12.org The names “CK-12” and “CK12” and associated logos and the terms “FlexBook®” and “FlexBook Platform®” (collectively “CK-12 Marks”) are trademarks and service marks of CK-12 Foundation and are protected by federal, state, and international laws. Any form of reproduction of this book in any format or medium, in whole or in sections must include the referral attribution link http://www.ck12.org/saythanks (placed in a visible location) in addition to the following terms. Except as otherwise noted, all CK-12 Content (including CK-12 Curriculum Material) is made available to Users in accordance with the Creative Commons Attribution-Non-Commercial 3.0 Unported (CC BY-NC 3.0) License (http://creativecommons.org/ licenses/by-nc/3.0/), as amended and updated by Creative Com- mons from time to time (the “CC License”), which is incorporated herein by this reference.
    [Show full text]