Syllabus for Geometry


Geometry

Syllabus 2016-2017

C. Reyna

creyna@sharylandisd.org

(956) 580-5300 ext 1219

 

 

Course Description:

Topics covered include the language of geometry (points, lines, planes and angles), reasoning and proofs (paragraph, two column, flow, indirect, and coordinate), parallel and perpendicular lines, congruent triangles, applications of congruent triangles, quadrilaterals, similarity, right triangles and trigonometry, circles, polygons and area, surface area and volume, coordinate geometry, and transformations.

 

Course Objective:

Students will acquire and demonstrate knowledge of concepts, definitions, properties, and applications of the topics listed above as well as develop the computational skills and strategies needed to solve problems. Students will develop critical thinking and decision making skills by connecting concepts to practical applications.

 

Grading:

60% Major Assignments: Tests, Reports, Projects

40% Minor Assignments: Classwork, Homework, Quizzes, Binders

**see district grading policy for specifications**

                                   

Required Materials:                                                Expectations:        

  • Loose leaf paper/Folder or Binder                 *Be on time and prepared
  • Pencil &colored pencils                                   *Be respectful
  • Compass & protractor                                     *No horse playing
  • Composition book (graph paper)                    *Bring your workbook and supplies
  • Batteries/Hand sanitizer/ Tissues                    *Follow School Rules

 

Tutoring:  Monday and Wednesday 4:00-4:30 or by appointment.

     My conference time is 3rd Block 11:21-12:51.

 

Course Schedule:  This is tentative and subject to change.

 

Unit 1:  Logical Argument and Constructions; Proofs and Congruence

 

Topic 1:  Tools of Geometry

            1-1:  Points, Lines, and Planes

            1-2:  Measuring Segments

            1-3:  Measuring Angles

            1-4:  Exploring Angle Pairs

            1-5:  Basic Constructions

 


Topic 2:  Reasoning and Proof

 

            2-1:  Patterns and Conjectures

            2-2:  Conditional Statements

            2-3:  Biconditional and Definitions

            2-4:  Deductive Reasoning

            2-5:  Reasoning in Algebra and Geometry

            2-6:  Proving Angles Congruent

 

Topic 3:  Parallel and Perpendicular Lines

 

            3-1:  Lines and Angles

            3-2:  Properties of Parallel Lines

            3-3:  Proving Lines Parallel

            3-4:  Parallel and Perpendicular Lines

            3-5:  Parallel Lines and Triangles

            3-6:  Constructing Parallel and Perpendicular Lines

            3-7:  Equations of Lines in the Coordinate Plane

            3-8:  Slopes of Parallel and Perpendicular Lines

            3-9:  Comparing Spherical and Euclidean Geometry

 

Topic 4:  Congruent Triangles

 

            4-1:  Congruent Figures

            4-2:  Triangle Congruence by SSS and SAS

            4-3:  Triangle Congruence by ASA and AAS

            4-4:  Using Corresponding Parts of Congruent Triangles

            4-5:  Isosceles and Equilateral Triangles

            4-6:  Congruence in Right Triangles

            4-7:  Congruence in Overlapping Triangles

 

Topic 5:  Relationships Within Triangles

 

            5-1:  Midpoint and Distance in the Coordinate Plane

            5-2:  Midsegments of Triangles

            5-3:  Perpendicular and Angle Bisector

            5-4:  Bisectors in Triangles

            5-5:  Medians and Altitudes

            5-6:  Indirect Proof

            5-7:  Inequalities in One Triangle

            5-8:  Inequalities in Two Triangles

 

 

Topic 6:  Polygons and Quadrilaterals

 

            6-1:  The Polygon Angle-Sum Theorems

            6-2:  Properties of Parallelograms

            6-3:  Proving That a Quadrilateral Is a Parallelogram

            6-4:  Properties of Rhombuses, Rectangles, and Squares

            6-5:  Conditions for Rhombuses, Rectangles, and Squares

            6-6:  Trapezoids and Kites

 

Unit 2:  Coordinate and Transformational Geometry

 

Topic 7:  Coordinate Geometry

 

            7-1:  Polygons in the Coordinate Plane

            7-2:  Applying Coordinate Geometry

            7-3:  Proofs Using Coordinate Geometry

 

Topic 8:  Transformational Geometry

 

            8-1:  Translations

            8-2:  Reflections

            8-3:  Rotations

            8-4:  Symmetry

            8-5:  Compositions of Rigid Transformations

            8-6:  Congruence Transformations

            8-7:  Dilations

            8-8:  Other Non-Rigid Transformations

 

Unit 3:  Similarity, Proof, and Trigonometry

 

Topic 9:  Similarity

 

            9-1:  Similar Polygons

            9-2:  Similarity Transformations

            9-3:  Proving Triangles Similar

            9-4:  Similarity in Right Triangles

            9-5:  Proportions in Triangles

 

Topic 10:  Right Triangles and Trigonometry

 

            10-1:  The Pythagorean Theorem and Its Converse

            10-2:  Special Right Triangles

            10-3:  Trigonometry

            10-4:  Angles of Elevation and Depression

 

Unit 4:  Circles

 

Topic 11:  Circle Measurement

 

            11-1:  Circles and Arcs

            11-2:  Radian Measure

            11-3:  Areas of Circles and Sectors

            11-4:  Circles in the Coordinate Plane

 

Topic 12:  Theorems About Circles

 

            12-1:  Tangent Lines

            12-2:  Chords and Arcs

            12-3:  Inscribed Angles

            12-4:  Angle Measures and Segment Lengths

 

Unit 5:  Two-Dimensional And Three-Dimensional Figures

 

Topic 13:  Area

 

            13-1:  Areas of Parallelograms and Triangles

            13-2:  Areas of Trapezoids, Rhombuses, and Kites

            13-3:  Areas of Regular Polygons

            13-4:  Perimeters and Areas of Similar Figures

            13-5:  Trigonometry and Area

 

Topic 14:  Surface Area and Volume

 

            14-1:  Three-Dimensional Figure and Cross Sections

            14-2:  Surface Areas of Prisms and Cylinders

            14-3:  Surface Areas of Pyramid and Cones

            14-4:  Volumes Prisms and Cylinders

            14-5:  Volumes of Pyramids and Cones

            14-6:  Surface Areas and Volumes of Spheres

            14-7:  Surface Areas and Volumes of Related Solids

 

Unit 6:  Probability

 

Topic 15:  Probability

 

            15-1:  Experimental and Theoretical Probability

            15-2:  Geometric Probability

            15-3:  Permutations and Combinations

            15-4:  Compound Probability

            15-5:  Conditional Probability With Frequency Tables

            15-6:  Conditional Probability Formulas