Course Overview
Students learn to recognize and work with geometric concepts in various contexts. They build on ideas of inductive and deductive reasoning, logic,
concepts, and techniques of Euclidean plane and solid geometry and develop an understanding of mathematical structure, method, and applications of
Euclidean plane and solid geometry. Students use visualizations, spatial reasoning, and geometric modeling to solve problems. Topics of study include
points, lines, and angles; triangles; right triangles; quadrilaterals and other polygons; circles; coordinate geometry; threedimensional solids; geometric
constructions; symmetry; the use of transformations; and nonEuclidean geometries. This is the second semester of MTH204.
This course includes all the topics in MTH203, but has more challenging assignments and includes more optional challenge activities. Each semester also
includes an independent honors project.
Course Outline
SEMESTER ONE
Unit 1: An Introduction
Even the longest journey begins with a single step. Any journey into the world of geometry begins with the basics. Points, lines, segments, and angles are
the foundation of geometric reasoning. This unit provides students with basic footing that will lead to an understanding of geometry.

Semester Introduction

Basic Geometric Terms and Definitions

Measuring Length

Measuring Angles

Bisectors and Line Relationships

Relationships between Triangles and Circles

Transformations

Using Algebra to Describe Geometry
Unit 2: Methods of Proof and Logic
Professionals use logical reasoning in a variety of ways. Just as lawyers use logical reasoning to formulate convincing arguments, mathematicians use
logical reasoning to formulate and prove theorems. With definitions, assumptions, and previously proven theorems, mathematicians discover and prove new
theorems. It's like building a defense, one argument at a time. In this unit, students will learn how to build a defense from postulates, theorems, and
sound reasoning.

Reasoning, Arguments, and Proof

Conditional Statements

Compound Statements and Indirect Proof

Definitions and Biconditionals

Algebraic Logic

Inductive and Deductive Reasoning
Unit 3: Polygon Basics
You can find polygons in many places: artwork, sporting events, architecture, and even in roads. In this unit, students will discover symmetry, work with
special quadrilaterals, and work with parallel lines and slopes.

Polygons and Symmetry

Quadrilaterals and Their Properties

Parallel Lines and Transversals

Converses of Parallel Line Properties

The Triangle Sum Theorem

Angles in Polygons

Midsegments

Slope
Unit 4: Congruent Polygons and Special Quadrilaterals
If two algebraic expressions are equivalent, they represent the same value. What about geometric shapes? What does it mean for two figures to be
equivalent? A pair of figures can be congruent the same way that a pair of algebraic expressions can be equivalent. You will learn, use, and prove theorems
about congruent geometric figures.

Congruent Polygons and Their Corresponding Parts

Triangle Congruence: SSS, SAS, and ASA

Isosceles Triangles and Corresponding Parts

Triangle Congruence: AAS and HL

Using Triangles to Understand Quadrilaterals

Types of Quadrilaterals

Constructions with Polygons

The Triangle Inequality Theorem
Unit 5: Perimeter, Area, and Right Triangles
If we have a figure, we can take many measurements and calculations. We can measure or calculate the distance around the figure (the perimeter or
circumference), as well as the figure's height and area. Even if we have just a set of points, we can measure or calculate the distance between two points.

Perimeter and Area

Areas of Triangles and Quadrilaterals

Circumference and Area of Circles

The Pythagorean Theorem

Areas of Special Triangles and Regular Polygons

Using the Distance Formula

Proofs and Coordinate Geometry
Unit 6: Semester Review and Test

Semester Review

Semester Test
SEMESTER TWO
Unit 1: ThreeDimensional Figures and Graphs
Onedimensional figures, such as line segments, have length. Twodimensional figures, such as circles, have area. Objects we touch and feel in the real
world are threedimensional; they have volume.

Semester Introduction

Solid Shapes and ThreeDimensional Drawing

Lines, Planes, and Polyhedra

Prisms

Coordinates in Three Dimensions

Equations of Lines and Planes in Space
Unit 2: Surface Area and Volume
Every threedimensional figure has surface area and volume. Some figures are more common and useful than others. Students probably see pyramids, prisms,
cylinders, cones, and spheres every day. In this unit, students will learn how to calculate the surface area and volume of several common and useful
threedimensional figures.

Surface Area and Volume

Surface Area and Volume of Prisms

Surface Area and Volume of Pyramids

Surface Area and Volume of Cylinders

Surface Area and Volume of Cones

Surface Area and Volume of Spheres

ThreeDimensional Symmetry
Unit 3: Similar Shapes
A map of a city has the same shape as the original city, but the map is much, much smaller. A mathematician would say that the map and the city are
similar. They have the same shape but are different sizes.

Dilations and Scale Factors

Similar Polygons

Triangle Similarity

SideSplitting Theorem

Indirect Measurement and Additional Similarity Theorems

Area and Volume Ratios
Unit 4: Circles
Students probably know what a circle is and what the radius and diameter of a circle represent. However, a circle can have many more figures associated
with it. Arcs, chords, secants, and tangents all provide a rich set of figures to draw, measure, and understand.

Chords and Arcs

Tangents to Circles

Inscribed Angles and Arcs

Angles Formed by Secants and Tangents

Segments of Tangents, Secants, and Chords

Circles in the Coordinate Plane
Unit 5: Trigonometry
Who uses trigonometry? Architects, engineers, surveyors, and many other professionals use trigonometric ratios such as sine, cosine, and tangent to compute
distances and understand relationships in the real world.

Tangents

Sines and Cosines

Special Right Triangles

The Laws of Sines and Cosines
Unit 6: Beyond Euclidian Geometry
Some people break rules, but mathematicians are usually very good at playing by them. Creative problemsolvers, including mathematicians, create new rules,
and then play by their new rules to solve many kinds of problems.

The Golden Rectangle

Taxicab Geometry

Graph Theory

Topology

Spherical Geometry

Fractal Geometry

Projective Geometry

Computer Logic
Unit 7: Semester Review and Test

Semester Review

Semester Test