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
Perspective (graphical) wikipedia , lookup
Cartesian coordinate system wikipedia , lookup
Trigonometric functions wikipedia , lookup
Multilateration wikipedia , lookup
Geometrization conjecture wikipedia , lookup
Rational trigonometry wikipedia , lookup
Euler angles wikipedia , lookup
Integer triangle wikipedia , lookup
History of trigonometry wikipedia , lookup
Pythagorean theorem wikipedia , lookup
History of geometry wikipedia , lookup
2015-2016 Geometry 2nd Quarter Mathematics Scope and Sequence Unifying Concept: Triangles and Quadrilaterals Mathematics Content Focus: Mathematical Practice Focus (Chapters 2,3,4, 5) Mathematically Proficient Students… Students will use inductive and deductive reasoning to 1. Make sense of problems and persevere in solving prove theorems about lines and angles them. 2. Reason abstractly and quantitatively. Students will investigate angles formed by parallel 3. Construct viable arguments and critique the reasoning lines and transversals. Students will also learn the of others. criteria for parallel and perpendicular lines and use 4. Model with mathematics. them to solve geometric problems. 5. Use appropriate tools strategically. 6. Attend to precision. Students will also prove theorems about triangles 7. Look for and make use of structure. involving interior angles and bisectors of triangles. 8. Look for and express regularity in repeated reasoning. Students use logic to identify the criteria for triangles to be congruent. Students will prove and apply theorems about perpendicular bisectors, angle bisectors, medians, and triangle midsegment theorem. Target Standards G.CO.B.6 Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent. G-CO.B.7 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. G-CO.B.8 Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions. G-CO.C.9 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. Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, √3) lies on the circle centered at the origin and containing the point (0, 2). G-GPE.B.5 Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). Quarter Major Clusters Arizona considers Major Clusters as groups of related standards that require greater emphasis than some of the others due to the depth of the ideas and the time it takes to master these groups of related standards. G-CO.B Understand congruence in terms of rigid motions Essential Concepts Essential Questions A rigid motion is a transformation of points in space How do you determine if two figures are consisting of a sequence of one or more translations, congruent? reflections, and/or rotations. What has to be true in order for two triangles to Rigid motions are assumed to preserve distances and be congruent? angle measures. How do the criteria for triangle congruence Congruent triangles have corresponding sides and (ASA, SAS, and SSS) follow from the definition corresponding angles that are congruent. of congruence in terms of rigid motions? The criteria for triangle congruence (ASA, SAS, and Why does SSA not work to prove triangle SSS) follow from the definition of congruence in terms congruence? of rigid motions. 8/28/2015 9:56 AM Curriculum Instruction and Professional Development Math Department Page 1 G-GPE.A.4 2015-2016 Geometry 2nd Quarter Mathematics Scope and Sequence G-CO.C Prove geometric theorems Essential Concepts: Essential Questions: A theorem is a statement that can be proven from How is a theorem different from an axiom? previously known facts, including postulates, axioms What is the difference between an axiom and a and definitions. postulate? A proof is a logical argument that shows that a How do you know when a proof is complete and theorem is true based on given information. valid? Properties of the sides and angles of geometric figures can be stated as theorems and proven. Several examples are listed in the standards. G-GPE.B Use coordinates to prove simple geometric theorems algebraically Essential Concepts Essential Questions Coordinate geometry can be used to solve simple How do you determine if two lines are parallel, geometric theorems algebraically. perpendicular or neither? Coordinate geometry can be used to prove that Given an equation of a line and a point not on the parallel lines have the same slope and perpendicular line, how do you write the equation of a line that lines have opposite reciprocal slopes. is parallel to the given line and through the given point? Perpendicular? How are geometry and algebra related to each other? 8/28/2015 9:56 AM Curriculum Instruction and Professional Development Math Department Page 2