### 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.

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

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

11-3:  Areas of Circles and Sectors

11-4:  Circles in the Coordinate Plane

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