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Unit Map 2012-2013 EdPower Shah, Ronak / Geometry (M) / Grade 9 (Tindley Accelerated School) Tuesday, June 25, 2013, 8:29AM Unit: Unit 3: Triangles (Week 8, 3 Weeks) Taught Curriculum Stage 1 - Desired Results Established Goals IN: CCSS: Mathematics, IN: HS: Geometry, Congruence G-CO Prove geometric theorems 10. Prove theorems about triangles. G-CO Make geometric constructions 12. Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line. 13. Construct an equilateral triangle, a square and a regular hexagon inscribed in a circle. IN: CCSS: Mathematics, IN: HS: Geometry, Circles G-C Understand and apply theorems about circles 3. Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle. IN: CCSS: Mathematics, IN: HS: Geometry, Modeling with Geometry G-MG Apply geometric concepts in modeling situations 1. Use geometric shapes, their measures and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).★ Key Words/Vocabulary Proof: A set of rigorous reasoning that guarantees the truth or falsehood of a statement. Triangle: A polygon with three vertices and three edges. Equilateral: A shape where all sides are line segments of equal length. Isosceles: A triangle where two legs are line segments of equal length. Interior Angles: The measures of the angles on the inside of a shape. Base Angles: The angles directly adjacent to the base of a shape. Midpoint: The point that divides a line segment into two congruent halves. Median: The line segment joining a vertex to the midpoint of the opposite side. Altitude: The line segment perpendicular to the base of a triangle. Circumscribe: To draw a circle that passes through all the vertices of a polygon. Inscribe: To draw a circle that passes through all the edges of a polygon. Essential Questions Understandings When a vertex, side, or angle is changed in a triangle, how is the triangle affected? Students will understand… What is the relationship between a triangle and more complex shapes? How can properties of triangles be modeled with realworld objects? Key Knowledge The circle inscribed in a polygon will always be smaller than that which circumscribes it. If the smaller sides of a triangle sum to the larger side, the triangle degenerates to a line. The properties of the sides of a triangle allow us to prove statements about its angles. The properties of the angles of a triangle allow us to prove statements about its sides. Because mathematics is a logical system, we can prove statements indirectly by assuming the opposite and creating a contradiction. Key Skills Students will know that… Students will be able to… The measures of the interior angles of a triangle sum to 180 degrees. The base angles of an isosceles triangle are congruent to each other. A bisector separates a line segment into two congruent line segments and an angle into two congruent angles. A perpendicular bisector separates a straight angle into two congruent right angles. The medians of a triangle meet at a point. The bisectors of a triangle meet at a point. Use tools to construct equilateral triangles and inscribed and circumscribed circles. Use a straightedge, protractor, and compass to copy and bisect angles and line segments. Identify patterns and make inductive conjectures about the properties of triangles. Use a proof to support a logical argument and prove a theorem about triangles. Prove a theorem using an indirect proof. Stage 2 - Assessment Evidence Evidence of Student Understanding Unit 3 Test -- Triangles Summative: Test: Standardized Unit 3 Test and Key.pdf Stage 3 - Learning Plan Detailed Unit Plan Learning Ladder Lesson Plan Unit 3 Calendar - Triangles.docx Syllabi Attach your syllabi with Links Resources Unit Reflection Last Updated: Tuesday, June 25, 2013, 8:28AM Atlas Version 7.2.6 © Rubicon International 2013. All rights reserved