Englewood Public School District Geometry Second Marking Period Unit 2: Polygons, Triangles, and Quadrilaterals Overview: During this unit, students will learn how to prove two triangles are congruent, relationships between angle measures and side lengths within a triangle, and about different types of quadrilaterals. Time Frame: 35 to 45 days (One Marking Period) Enduring Understandings: • Congruent triangles can be visualized by placing one on top of the other. • Corresponding sides and angles can be marked using tic marks and angle marks. • Theorems can be used to prove triangles congruent. • The definitions of isosceles and equilateral triangles can be used to classify a triangle. • The Midpoint Formula can be used to find the midsegment of a triangle. • The Distance Formula can be used to examine relationships in triangles. • Side lengths of triangles have a relationship. • The negation statement can be proved and used to show a counterexample. • The diagonals of a polygon can be used to derive the formula for the angle measures of the polygon. • The properties of parallel and perpendicular lines can be used to classify quadrilaterals. • Coordinate geometry can be used to classify special parallelograms. • Slope and the distance formula can be used to prove relationships in the coordinate plane. Essential Questions: • How do you identify corresponding parts of congruent triangles? • How do you show that two triangles are congruent? • How can you tell if a triangle is isosceles or equilateral? • How do you use coordinate geometry to find relationships within triangles? • How do you solve problems that involve measurements of triangles? • How do you write indirect proofs? • How can you find the sum of the measures of the angles of a polygon? • How can you classify quadrilaterals? • How can you use coordinate geometry to prove general relationships? Standards Topics and Objectives Activities Materials/Resources Assessments Topics NJSLA Geometry Lessons: Pearson Realize Chapters 4, Formative G-CO.C.9 Prove theorems • Determining 5, and 6 Assessments: about lines and angles. Congruence, Corresponding Congruence: The Case Textbook Pages 243, parts of congruent figures, Study of a Triangle NJSLA Lessons (Shared 277, 278, 316, 345, 346, G-CO.C.10 Prove theorems triangle congruence • Proving Parallelogram Folder) 398, 425, 426 about triangles. theorems, isosceles and Theorems equilateral triangles, • Proving Triangle Illustrative Mathematics Math journal G-CO.C.11 Prove theorems midsegments of triangles, Theorems https://www.illustrativemath (NJSLSA.W10, about parallelograms. altitudes and medians of ematics.org/ NJSLSA.L1, triangles, perpendicular and Is this a Rectangle? NJSLSA.L6) G-CO.D.12 Make formal angle bisectors, inequalities https://www.illustrativemat National Library of Virtual geometric constructions in triangles, quadrilaterals, hematics.org/content- Manipulatives Summative with a variety of tools and parallelograms, rectangles, standards/HSG/CO/B/tasks http://nlvm.usu.edu/ Assessments: methods rhombi, squares, trapezoids, /1302 (MP4) Multiple choice / short kites, and quadrilaterals in Alabama Learning answer assessments G-CO.D.13 Construct an the coordinate plane Are the Triangles Exchange (CRP2, CRP4, CRP8) equilateral triangle, a Congruent? http://alex.state.al.us/search. square, and a regular Objectives https://www.illustrativemat php?fa_submit=ALLPLAN Chapter quizzes/tests hexagon inscribed in a hematics.org/content- S • Pearson Realize circle. Students will standards/HSG/CO/B/tasks • MathXL • prove theorems about /33 (MP4) NYC Department of G-SRT.B.5 Use congruence lines and angles Education Benchmark and similarity criteria for • prove vertical angles Properties of Congruent http://schools.nyc.gov/defau Assessment: triangles to solve problems are congruent Triangles lt.htm Midterm Assessment and to prove relationships • prove that when a https://www.illustrativemat in geometric figures. transversal crosses hematics.org/content- Mathematics Assessment Alternative parallel lines, standards/HSG/CO/B/7/tas Project Assessments: G-C.A.3 Construct the alternate interior ks/1637 (MP1) http://map.mathshell.org/ Learning centers: each inscribed and angles are congruent learning center focuses circumscribed circles of a • prove that when a SSS Congruence Criteria Texas Instruments on a different type of triangle, and prove transversal crosses https://www.illustrativemat https://education.ti.com/en/u problem properties of angles for a parallel lines, hematics.org/content- s/home quadrilateral inscribed in a corresponding angles standards/HSG/CO/B/8/tas Create posters circle. are congruent ks/1930 (MP4) Desmos illustrating the main • prove measures of the https://teacher.desmos.com/ objectives of the unit G-GPE.B.4 Use coordinates interior angles of a When does SSA work for (CRP6) to prove simple geometric triangle sum to 180 Triangle Congruence? 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(CRP2, CRP4, CRP8, MP2 Reason abstractly and geometric tools and https://www.illustrativemat 8.1.12.A.3) quantitatively. methods to construct hematics.org/content- MP3 Construct arguments perpendicular lines, standards/HSG/CO/B/8/tas Geometry NJSLS and critique the reasoning of including ks/109 (MP7) worksheets: others. perpendicular https://www.ixl.com/math/g MP4 Model Mathematics. bisectors Why does SSS work? eometry MP6 Attend to precision. • use a variety of https://www.illustrativemat (CRP2, CRP4, CRP8) MP7 Look for and make use geometric tools and hematics.org/content- of structure. methods to construct standards/HSG/CO/B/8/tas Khan Academy – videos, MP8 Look for and express a line parallel to a ks/110 (MP4) lessons, assessments regularity in represented given line through a www.khanacademy.org reasoning. point not on the line Congruent Angles in (CRP2, CRP4, CRP8, • construct an Isosceles Triangles CRP11, 8.1.12.A.3) equilateral triangle https://www.illustrativemat inscribed in a circle hematics.org/content- Worksheets / assessment standards/HSG/CO/C/10/ta items for all topics based on • construct a regular sks/1921 (MP4) standards: hexagon inscribed in http://jmap.org/JMAP_RES a circle Midpoints of Triangle OURCES_BY_TOPIC.htm • construct a square Sides #AI(CRP2, CRP4, CRP8) inscribed in a circle https://www.illustrativemat • use the definition of hematics.org/content- similarity in terms of standards/HSG/CO/C/10/ta similarity sks/1872 (MP2) transformations to decide if two given figures are similar Is this a Parallelogram? • explain, using https://www.illustrativemat similarity hematics.org/content- transformations, the standards/HSG/CO/C/11/ta meaning of similarity sks/1321 (MP1) for triangles as the equality of all Midpoints of the Sides of a corresponding pairs Parallelogram of angles and the https://www.illustrativemat proportionality of all hematics.org/content- corresponding pairs standards/HSG/CO/C/11/ta of sides sks/35 (MP4) • construct the inscribed and What do you know about circumscribed circles the Bermuda Triangle? of a triangle http://alex.state.al.us/lesson • prove properties of _view.php?id=33167 angles for a (MP1) quadrilateral inscribed in a circle Triangle Midsegments • prove simple https://education.ti.com/en/ geometric theorems us/activity/detail?id=BD84 algebraically using 0BAD7E754B7BB0B5A2 coordinates ECB79A2107&ref=/en/us/ • compute perimeter of activity/search/advanced polygons using (MP6) coordinates • compute areas of Exterior and Remote rectangles using Interior Angles coordinates https://education.ti.com/en/ • compute area of us/activity/detail?id=A0F8 triangles using CB43E61B430B8882100C coordinates 56D8AA09&ref=/en/us/act ivity/search/advanced (MP2) Properties of Parallelograms https://education.ti.com/en/ us/activity/detail?id=5CDF 181BDFBE42BB8FC1070 63B5EBA08&ref=/en/us/a ctivity/search/advanced (MP2) Triangle Sides and Angles https://education.ti.com/en/ us/activity/detail?id=64E71 D93C94F43C0968730A66 24B30BF&ref=/en/us/activ ity/search/advanced(MP7) Properties of Special Quadrilaterals https://education.ti.com/en/ us/activity/detail?id=3EFE CCEBAFA04B6990D369 A41FA4F83F&ref=/en/us/ activity/search/advanced (MP2) Creating a Parallelogram https://education.ti.com/en/ us/activity/detail?id=CA35 3F7DA7034A878EDA599 7128351B2&ref=/en/us/act ivity/search/advanced (MP6) Properties of Trapezoids and Kites https://education.ti.com/en/ us/activity/detail?id=F33C 9C7C2E8842BEB300C582 7F081E93&ref=/en/us/acti vity/search/advanced (MP8) Congruent or Not? https://education.ti.com/en/ us/activity/detail?id=E0879 6D0158C40B2A507501D0 B66E8A7&ref=/en/us/activ ity/search/advanced(MP6) Rhombi, Kites, and Trapezoids https://education.ti.com/en/