Geometry Syllabus 2020-2021

Teacher: J. Vela

Phone: (956) 271-1600 ext. 4169


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:

• 1 subject notebook/composition *Be on time

• Post it 3 inch by 3 inch   *Be Respectful

• protractor     *No Horseplay

• Glue bottle                                                               *Bring supplies   

• Glue bottle                                                              *Follow School Rules 

• 500 index cards

• 2 boxes of Markes

  • Ream of colored construction paper

Materials for projects I will let you know when to bring them.

• 2 white poster boards (Dollar tree)

• White foam board (Dollar tree or Walmart)

• 1 Yarn

• Canvas needle (Walmart or Michaels)

Tutoring: TBA

Conference: 5th Block 2:30 – 4:00



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


Advanced Quantitative Reasoning

Semester  Syllabus



Welcome to AQR!  This is an exciting and dynamic course in which we will work together to explore ways that math is used in the “Real World”.  This course requires that you use all the skills learned in Algebra I, Geometry, and Algebra II in order to investigate and solve application problems.  We are very excited about this class and hope to have an amazing year.




First Semester Topics Covered / Units of Study


     Unit I: Analyzing Numerical Data

       Using Ratios, Rates, and Percents

       Using Averages, Weighted Averages, and Indices

       Estimating Large Numbers

       Using Check Digits to Validate Identification Numbers

     Unit II: Probability

       Determining Probabilities

       Everyday Decisions Based on Probabilities

       Expected Value

     Unit III: Mathematical Models

       Recursive Rules

       Explicit Rules

       Modelling with Linear and Exponential Functions

       Modelling with Step and Piecewise Functions

       Modelling with Cyclical Functions



            All students will actively participate in class.

            All students will present work to class.

            All students will present work that reflects their best abilities.

            All students will be responsible to complete any outside work.

            All students will be challenged.

            All students will experience successful problem solving.



Attendance / Missed Assignments:

            AQR is a rigorous course and much of what we learn in this class will come from in-class projects, group discussions, and collaborative projects.  Regular attendance in this class is crucial to students’ success.  In the event of an absence, it is the student’s responsibility to obtain any missed / make-up work and turn it in within the same number of days that he / she was absent.  If a test or major project is missed, that student will be responsible for completing that on the day that they return.  If an absence occurs the class period before a test or project, the student will be required to complete the test or project on the assigned day since all major grade assignment dates are given at the beginning of each unit


Classroom Expectations:

      Come Prepared:  Be ready to learn; have paper, pen/pencil, book, planner, and homework. 

      Always Respectful: No talking back-use appropriate tone when speaking, no derogatory language or swearing, don’t speak out of turn; be polite to every person on campus.

      iN The Proper Place:  Be in class on time; don’t wander the building, have a hall pass, use the closest restroom.

      Engaged in Learning:  Participate, pay attention, take notes, complete class assignments, don’t interrupt when another person is speaking.

      Show Responsibility:  Complete assignments, turn in work on time, do your own work

      Cheating of any kind will not be tolerated.  Any student found guilty of cheating will receive an automatic zero on the assignment, test, or quiz.  The parent will be notified.  The assigned administrator may also be contacted.

      Sleeping, or the appearance of sleeping, will not be allowed




Contact Information: You may contact me by phone or email.