# Geometry

**Topics Covered**

· Points and Lines

· The Language and Logic of Geometry

· Angles and Lines

· Reflections and Congruence

· Proofs Using Congruence

· Polygons and Symmetry

· Triangle Congruence

· Perimeters and Areas

· Three-Dimensional Figures

· Surface Areas and Volumes

· Indirect and Coordinate Proofs

**Necessary Materials**

· Scientific calculator

· 3-ring binder with at least 4 dividers

· Pencil

· Ruler

**Expectations**

· Textbook and class materials are to be brought to class every day.

· Homework is to be completed, with all work neatly shown, and brought to class the day it is due. Reasons for failure to do work should be brought to the teacher’s attention via a note from the parents. All make-up work should be completed as soon as possible.

· Students need to come to class on time ready to participate.

**Grading**

· Class participation/preparation

· Homework is assigned daily and graded according to a homework rubric.Homeworkrubric.pdf

· Quizzes will occur on a regular basis and will be announced at least one day in advance.

· Tests will occur at the end of each chapter.

· Portfolio tasks are assigned at least once a month. Each portfolio counts as a test grade and is graded according to a rubric.

· Notebooks are graded at least once per quarter as a test grade. They are graded on completeness, organization, vocabulary and notes from class, using a notebook rubric.Notebookrubric.pdf

· Mid-year and final exams will be given.

· Late work will be accepted up to 2 weeks past the due date with the following penalties: A loss of 10% of the grade for that assignment per day for the first week and 50% of the grade for that assignment during the second week. At the end of two weeks, the assignment is a 0% and may not be turned in for credit.

**Course Outline**

I) Points and Lines

A) Dots as Points

B) Locations as Points

C) Ordered Pairs as Points

D) Points in Networks

E) Drawing in Perspective

F) The Need for Undefined Terms

G) Postulates for Euclidean Geometry

H) Betweenness and Distance

II) The Language and Logic of Geometry

A) The Need for Definitions

B) "If-Then" Statements

C) Converses

D) Good Definitions

E) Unions and Intersections of Figures

F) Polygons

G) The Triangle Inequality

H) Conjectures

III) Angles and Lines

A) Angles and Their Measures

B) Arcs and Rotations

C) Properties of Angles

D) Algebra Properties Used in Geometry

E) One-Step Proof Arguments

F) Parallel Lines

G) Perpendicular Lines

H) Drawing Parallel and Perpendicular Lines

IV) From Reflections to Congruence

A) Reflecting Points

B) Reflecting Figures

C) Minature Golf and Billiards

D) Composing Reflections over Parallel Lines

E) Composing Reflections over Intersecting Lines

F) Translations and Vectors

G) Isometries

H) When Are Figures Congruent?

V) Proofs Using Congruence

A) Corresponding Parts of Congruent Figures

B) Congruence and Equality

C) One-Step Congruence Proofs

D) Proofs Using Transitivity

E) Proofs Using Reflections

F) Auxiliary Figures and Uniqueness

G) Sums of Angle Measures in Polygons

VI) Polygons and Symmetry

A) Reflection-Symmetric Figures

B) Isosceles Triangles

C) Types of Quadrilaterals

D) Properties of Kites

E) Properties of Trapezoids

F) Rotation Symmetry

G) Regular Polygons

H) Regular Polygons and Schedules

VII) Triangle Congruence

A) Drawing Triangles

B) Triangle Congruence Theorems

C) Proofs Using Triangle Congruence Theorems

D) Overlapping Triangles

E) The SSA Condition and HL Congruence

F) Tessellations

G) Properties of Parallelograms

H) Sufficient Conditions for Parallelograms

I) Exterior Angles

VIII) Perimeters and Areas

A) Perimeter Formulas

B) Fundamental Properties of Area

C) Areas of Irregular Regions

D) Areas of Triangles

E) Areas of Trapezoids

F) The Pythagorean Theorem

G) Arc Length and Circumference

H) The Area of a Circle

VIII) Three-Dimensional Figures

A) Points, Lines, and Planes in Space

B) Parallel and Perpendicular Lines and Planes

C) Prisms and Cylinders

D) Pyramids and Cones

E) Spheres and Sections

F) Reflection Symmetry in Space

G) Viewing Solids and Surfaces

H) Making Surfaces

I) Maps and the Four Color Theorem

X) Surface Areas and Volumes

A) Surface Areas of Prisms and Cylinders

B) Surface Areas of Pyramids and Cones

C) Fundamental Properties of Volume

D) Multiplication, Area, and Volume

E) Volumes of Prisms and Cylinders

F) Organizing Formulas

G) Volumes of Pyramids and Cones

H) The Volume of a Sphere

I) The Surface Area of a Sphere