Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Multilateration wikipedia , lookup
Cartan connection wikipedia , lookup
Trigonometric functions wikipedia , lookup
Rational trigonometry wikipedia , lookup
Geometrization conjecture wikipedia , lookup
Euler angles wikipedia , lookup
Pythagorean theorem wikipedia , lookup
History of trigonometry wikipedia , lookup
Line (geometry) wikipedia , lookup
Integer triangle wikipedia , lookup
EAST ALLEN COUNTY SCHOOLS Bundle 2 Geometry Congruence in Proofs Big Idea: Deductive Reasoning Enduring Understandings Essential Questions Relationships between angles and sides can be used to prove the congruence of triangles. Properties of parallelograms and triangles have useful real-world applications. Congruent geometric figures are modeled through constructions using a specific sequence of steps and processes. CC/Learning Targets G.CO.7 G.CO.8 G.CO.9 G.CO.10 G.CO.11 G.CO.12 G.CO.13 What rotation, reflection and/or translation transforms figures while maintaining congruence? What relationships do angles and sides have in proving triangle congruence? What is special about angles formed by two or more lines? What are the properties of special parallelograms? What are the properties of special triangles? How would you use constructions and the coordinate plane to represent geometric figures? Core Vocabulary Links to Technology alternate interior/exterior angles biconditional statement conditional statement corresponding angles negation theorem transversal Bundle Performance Task(s) Students will create a board game (monopoly, clue, chutes and ladders, life) that will have questions pertaining to the following topics: Statement/justifications of proof Properties of parallelograms Properties of special triangles Properties of special angle pairs Congruence of triangles Misc. The game is to last a minimum of 15 – 30 minutes. All supplies needed to play the game are to be included. A list of questions with answers is to be submitted with the game. A possible assessment rubric is provided in the Appendix under Curriculum for each Performance Task. Geometry Bundle 2 Quarter 1 Sept.-Oct. Geometry CC/Learning Targets G.CO.7 (G.4.3a) G.CO.8 (G.4.6c) G.CO.9 (G1.2f) (G.1.3a-d) (G.8.8a) G.CO.10 (G.4.1a-b) (G.4.2a-b) (G.4.9a-b) (G.8.8a) Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent. Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions. Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints. Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a Bundle 2 Resource of Ideas -AAS Congruence -HL -ASA -SSA not enough information -SSS -SAS -Prentice Hall Mathematics Lessons 3.7, 4.2, 4.3, 4.6 -Triangle congruence -Prentice Hall Mathematics Lessons 4.2, 4.3, 4.6, 4.7 -Special angles when lines are parallel -Prentice Hall Mathematics Lessons 3.1, 3.2, 5.5 -iBook Prentice Hall Geometry Lessons 2.1-2.6, 3.1-3.3,5.2 -Proof of sum of angles in triangle is 180 -Isosceles triangles -Isosceles triangle proof-Kahn Academy -Midsegment of a triangle properties and uses -Special segment in triangle median -Point of concurrency median Evidence of Learning -Homework -White Boards -Entrance/Exit tickets -Nearpod -Journal -Homework -Quiz/Test -Worksheet -Journal -Proof -Patty Paper -Flash Card/Note Card -Quiz -Journal -Proof -Paddy Paper -Constructions -Homework -Journal Geometry G.CO.11 (G.2.3a) (G.3.1a) (G.3.1c-f) (G.3.4a-b) (G.8.8a) G.CO.12 (G.1.2b-e) (G.1.2g) (G.2.4d-e) (G.4.2c-f) (G.4.2h,I, k) (G.8.9a-c) G.CO.13 (G4.2d, j) (G.6.4a-b) (G7.6c) (G.8.9a) Bundle 2 triangle meet at a point. -Prentice Hall Mathematics Lessons 3.3, 5.3 -iBook Prentice Hall Geometry Lessons 2.1-2.5, 3.5, 4.5, 5.1, 5.4-5.7 Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals. 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. Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle. -Practice parallelogram proofs Correlating CC/Learning Targets -Entrance/Exit Ticket -Nearpod -White boards -Patty Paper -Flash Card/Note Card -Journal -Prentice Hall Mathematics Lessons 4.1, 4.4, 6.1, 6.2, 6.4, 6.6, 6.7, 8.6 -iBook Prentice Hall Geometry Lessons 2.1-2.5, 6.2-6.5 -Constructing a segment -Angle bisector -Constructions -Journal -Small Group Discussion -Quiz/Test -Prentice Hall Mathematics Lessons 1.5, 5.2, 5.3 -iBook Prentice Hall Geometry Lessons 1.6, 3.2, 3.6, 4,4 -Construction an equilateral triangle -Regular polygons inscribed in a circle -Construction -Journal -Quiz/Test -Patty Paper -Prentice Hall Mathematics Lessons 1.5, 5.3, 11.1 -iBook Prentice Hall Geometry Lessons 3.6, 4.5, 5.1, 10.3 Teacher Notes Geometry G.CO.1 G.CO.2 G.CO.3 G.CO.4 G.CO.5 G.CO.6 Bundle 2 G.GPE.5 G.GPE.6 All embedded apps included in this curriculum are free. iTunes U, Northest Arkasas Education Cooperative Geometry Lesson 6 Polygon Identification