SYLLABUS
Honors Geometry
INSTRUCTOR: Kenneth R Valiska SCHOOL YEAR: 2015-2016
COURSE
DESCRIPTION
EXPECTATIONS
CREDIT:
TIME: 2:15-3:10
COURSE NUMBER: 321
This course is designed to prepare talented mathematics students for success in all areas that require a rigorous
development of traditional Geometry topics. Students will relate and apply geometric concepts to algebra, statistics,
Data analysis, probability and discrete mathematics. . This course has a strong emphasis on formal proofs as well as
algebraic, paragraph, flowchart, andcoordinate proofs. Topics include points, lines and planes, the connection
between reasoning and proof, parallel & perpendicular lines, congruent triangles, polygons, proportions and similarity,
right triangle trigonometry,circle geometry, coordinate geometry and transformations. In addition, students will perform
actual measurements using both appropriate measuring instruments and geometric methods. Students will be expected
to bring a TI-30 scientific calculator/graphing calculator to class every day.
After successfully completing this course, the student will understand that
1. points, lines and planes are the essential building blocks for creating the shapes, dimensions and beauty of our world.
2. proportions and ratios, including trigonometric ratios, are used to create maps, artwork, architecture and many
other things in the real world.
3. polygons and circles are the fundamental building blocks for the aesthetic and structural world around us.
4. in order to form logical arguments, complex ideas are developed through the connection of smaller, previously
accepted or proven ideas.
5. measurement is used to describe and analyze the sizes, area and capacities of many things in our world
1 credit
AREAS OF
STUDY:
LEVEL:
First Semester
1
2
3
4
5
Introduction to Geometry
Basic Concepts and Proofs
Congruent Triangles
Lines in the Plane
Parallel Lines and Related Figures
9,10 - Honors
Second Semester
7
8
9
10
11
12
Polygons
Similar Polygons
Pythagorean Theorem/Trig/Law Sines & Cosines
Circles
Area
Surface Area & Volume
TIMELINES
Honors Geometry
First Semester
Suggested Timelines
Suggested Timelines
Chapter 1
Introduction to Geometry
14 days
Chapter 4
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.9
Getting Started (1) G-CO-1
Measurements of Segments, Angles & Clock Angles (2) G-CO-1
Collinearity, Betweenness and Assumptions (1) G-CO-9
Beginning Proofs (2) G-CO-9
Division of Segments and Angles (2) G-CO-9
Paragraph Proofs (1) G-CO-6
Deductive Structure (1)
Probability (1)
4.1
4.2
4.3
4.4
4.5
4.6
Common Assessment Quarter 1
Chapter 3
Congruent Triangles
16 days
3.1
What are Congruent Figures? (1) G-CO-4
3.2
Three Ways to Prove Triangles Congruent (2) G-CO-8
3.3
CPCTC and Circles (2) G-CO-7
3.4
Beyond CPCTC (2) G-CO-7
3.5
Overlapping Triangles (2) G-CO-7/8
3.6
Types of Triangles (1) G-CO-10
3.7
Angle-Side Theorems (2) G-CO-10
3.8
The HL Postulate (1) G-CO-8
5.2
5.3
5.4
5.5
5.6
5.7
10 days
Detours and Midpoints (1) G-CO-8
The Case of the Missing Diagram (1) G-CO-7/8
A Right-Angle Theorem (1) G-CO-9
The Equidistance Theorems (2) G-CO-9
Introduction to Parallel Lines (1) G-CO-9
Slope (2) G-GPE-5
Chapter 5
Chapter 2
Basic Concepts and Proofs
12 days
2.1
Perpendicularity (1) G-CO-1
2.2
Complementary and Supplementary Angles (1) G-CO-9
2.3
Drawing Conclusions (1) G-CO-9
2.4
Congruent Supplements and Complements (1) G-CO-9
2.5
Addition and Subtraction Properties (2) G-CO-9
2.6
Multiplication and Division Properties (2) G-CO-9
2.7
Transitive and Subtraction Properties (1) G-CO-9
2.8
Vertical Angles (1) G-CO-9
Lines in the Plane
Parallel Lines and Related Figures
12 days
Proving that Lines are Parallel (2) G-Co-9
Congruent Angles Associated with Parallel Lines (2) G-CO-9
Four-sided Polygons (2) G-CO-11
Properties of Quadrilaterals (2) G-CO-11
Proving that a Quadrilateral is a Parallelogram (2) G-CO-11
Proving that Figures are Special Quadrilaterals (2) G-CO-11
Number of Teaching Days
Review for Semester Exam
Common Assessment
Miscellaneous Days:
School Improvement, Assembly, Institute, Stand. Testing
TOTAL DAYS: (75)
56 days
2 days
1 day
11 days
_______
75 days
TIMELINES
Honors Geometry
Second Semester
Suggested Timelines
Chapter 7
7.1
7.2
7.3
7.4
7 days
10.3
10.4
10.5
10.6
10.7
10.9
12 days
Chapter 11
Area
10 days
11.1
Understanding Area (1) G-GMD-4
11.2
Areas of Parallelograms and Triangles (2) G-CO-10/11
11.3
The Area of a Trapezoid (2) G-GPE - 7
11.4
Areas of Kites and Related Figures (2) G-GPE-7
11.5
Areas of Regular Polygons (2) G-CO-13
11.6
Areas of Circles, Sectors, and Segments (2) G-GMD-1
Triangle Application Theorems (1) G-CO-10
Two Proof-oriented triangle Theorems (2) G-CO-8
Formulas Involving Polygons (1)
Regular Polygons (1) G-CO-13
Chapter 8
81
8.2
8.3
8.4
8.5
Polygons
Similar Polygons
Ratio & Proportion (2) A-REI-3
Similarity (1) G-SRT-2
Methods of Proving Triangles Similar (2) G-SRT-3
Congruences &Proportions in Similar Triangles (2) G-SRT-5
Three Theorems involving proportions (2) G-SRT-4
Arcs of a Circle (2) G-C-2
Secants & Tangents (1) G-C-4
Angles Related to a Circle (1) G-C-3
More Angle-Arc Theorems (2) G-C-3
Inscribed and Circumscribed Polygons (1) G-C-3
Circumference and Arc Length (1) G-GMD-1
Chapter 9
The Pythagorean Theorem
14days
9.1 Review of Radicals & quadratic equation (1) N-RN-3
9.2
Intro to Circle (1) G-C-2
9.3
Altitude-on-Hypotenuse (2) G-SRT-5
9.4
Geometry’s Most Elegant Theorem (1) G-CO-1
9.5
the distance formula (1) G-CO-1
9.7
Special Right Triangles (2) G-SRT-8
9.8
The Pythagorean Theorem & Space Figures (1) G-SRT-8
9.9
Introduction to Trigonometry (1) G-SRT-6/7
9.10
Trig Ratios (2)
Chapter 12
Number of teaching days
Common Assessment
63 days
1 day
COMMON ASSESSMENT Quarter 3
Review for Semester Exam
Miscellaneous Days
Total Days
2 days
19 days
90 days
Chapter 10
Circles
10.1
The Circle (1) G-C-2
10.2
Congruent Chords (2) G-C-2
13 days
12.1
12.2
12.3
12.4
12.5
12.6
Surface Area and Volume
Surface Area of Prisms (2) 7-G-6
Surface Area of Pyramids (2) 7-G-6
Surface Areas of Circular Solids (2) 8-G-9
Volumes of Prisms and Cylinders (2) G-GMD-3
Volumes of Pyramids and Cones (2) G-GMD-3
Volumes of Spheres (1) G-GMD-3
12 days