Geometry 2014-2015 Mrs. K Smith The Purpose of the geometry curriculum is to encourage student awareness of the importance of mathematics in the modern world. The course includes among other things, properties of geometric figures with reasoning to justify conclusions. Methods of justification will include paragraph proofs, twocolumn direct and indirect proofs coordinate proofs. The student will have the understanding of many theorems and how to deductively prove the theorems. The students will be able to use the concepts of the geometric theorems and apply them to an algebraic language. Course Outcome: Students will have been taught the NYS Geometry standards/and common core standards. All topics taught this year are listed below. Every student will take the NYS Geometry Regents and the Common Core Geometry exam in June. The exam with the higher grade will count as 20% of their final average. How to achieve mastery: - Student must have good attendance, if they are absent please get notes and assignment from that day. - Student must get extra help if they need it. -Student must complete all assignment s even if they are not graded (it is their way of practicing) Grading policy: Homework count 1 time, Quizzes count 2 times and tests count 3 times. There are occasional extra credit poster projects also. Materials Required: 5 subject notebook, folder, scientific or graphing calculator, compass, ruler. Syllabus-Geometry and Geometry Common Core Geometry Fundamentals -Points, lines, planes -Segments and rays -Angles Logic -Negation -conjunction -disjunction -conditional -biconditional
-inverse, converse, contrapositive Proving Statements -Inductive reasoning -Definitions as Biconditionals -Deductive reasoning -Direct proofs -Postulates, Theorems and proofs -Substitution, Addition, Subtraction postulates -Mult. and Division postulates Congruence of Line Segments, Angles and Triangles -Postulates of line, line segments, angles -Using postulate and definitions in proofs -Proving theorems about angles -Congruent polygons and corresponding parts -Proving triangles congruent using SSS, ASA, SAS Congruence Based on Triangles -Line segments associated with Triangles -Using corresponding parts of congruent triangles to prove other pairs of triangles congruent -Isosceles and equilateral triangle -Triangle pairs - Proving overlapping triangles -Perpendicular bisector of a line segment -Basic constructions -Concurrence of segments in/out of triangles Transformations (Rigid Motions)on the Coordinate Plane -Line reflections -Rotations -Dilations -Translations -Glide reflections -Transformations as functions and the composition of transformations Geometric Inequalities -Basic inequality theorem, add subtract mult and divide -Inequalities involving the lengths of the sides of a triangle -Inequality involving the exterior angle of a triangle -Inequalities involving the sides and angles of a triangle Slopes and Equations of lines -Slopes -Equation of a line -Midpoint of a line segment
-Slopes of perpendicular lines -Coordinate proof -Concurrence of altitudes in a triangle Parallel lines -Proving lines parallel -sum of the measures of the angle of a triangle proof -Proving triangles congruent by ASA -The converse of the isosceles triangle theorem -interior and exterior angle of polygons Quadrilateral -Quads -Parallelograms -Proving a quad is a parallelogram -The rectangle -Rhombus -Square -Trapezoid -Areas of polygons Right Triangle Trigonometry -Sine -Cosine -Tangent -Angle of depression -Angle of elevation Ratio, Proportion and Similarity -Means and extremes -solving proportions of lengths -Similar polygons -Proving polygons similar -Proving triangles proportional -Concurrence of medians in a triangle -Proportions in a right triangle -Pythagorean Theorem -Distance formula Geometry of the Circle -Arcs and angles -Arcs and chords -Inscribed angles and their measures -Area and sectors of circle -radian measure in a circle
-Angles formed by Tangents, secants and chords -Circle on the coordinate plane-equation of a circle Locus (not common core) and Constructions -The meaning of locus -The five fundamental Loci -Points at a fixed distance -Equidistant lines in coordinate geometry 3 Dimemsional Geometry -Points, lines and planes -Perpendicular lines and planes -Surface Area of prisms -Volume of prisms -Pyramids -Cylinders -Cones -Spheres -Cavelieri s Principle The 6 Domains in The Geometry Common Core are 1.Congruence 27-34% 2. Similarity, right triangles, TRIGONOMETRY (new) 29%-37% 3. Circles 2-8% 4. Expressing Geometric Properties with equation 12-18% 5. Geometric Measurement &Dimensions 2-8% 6. Modeling with Geometry 8-15% Note that all of these topics with the exception of right triangle trig, cavelieri principle and some minor vocabulary words added have been covered in past practice with the regular geometry standards from NYS. -
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