Class Description

Geometry is a branch of mathematics that involves studying shape, size, and position of geometric figurers. These include triangles and rectangles in plane (two-dimensions) cubes and spheres in solids (three-dimensions). The name Geometry means "measure the earth". Geometry is important because the world God created is full of geometric shapes. Snowflakes are sis-sided figures as are the honeycombs bees make. The rainbow is a circular shape and a light ray goes in a straight line.

 

Geometry has practical application in may fields. Architects and carpenters must understand the properties of geometric objects to construct strong and attractive buildings. Houses have rectangular walls and triangular rafters. Pilots and astronauts rely on geometric ides to plan and fly to their destination. Engineers and photographers use geometric principles in their work.

 

Deductive reasoning is important in the study of Geometry. Deductive reason begins with statements that are accepted as true and combines these in a logical way to reach additional conclusions. When the original statement is true, correct deductive reasoning always leads to true conclusions.

Class Expectations

Daily Assignments:

1. Assignments will be given daily.
2. Assignments will be corrected the following day by the student so they can receive immediate feed back on how they are doing.
3. Assignments are always passed in and scored by the teacher and not returned to the student.
4. Credit for the daily work is primarily given for the effort and amount of work shown.
5. Most students average 30 minutes a day on the daily work.

Tests:

1. Tests are given at the end of each chapter.
2. Grades will be determined by the accuracy of answers and the work shown.

Final Grade:

1. The nine week's grade is determined by having daily work counting 25%, quizzes counting 15%, and test grades counting 60% of the grade.
2. The semester grade is calculated as follows: first nine weeks 40%, second nine weeks 40% and the semester exam (20%).

Class Outline

A. Tools of Geometry

Inductive Reasoning
Points, Lines, and Planes
Measuring Segments and Angles
Basic Constructions
Coordinate Plane

B. Reasoning and Proof

Conditional Statements
Deductive Reasoning
Proving Angles Congruent

C. Parallel and Perpendicular Lines

Properties of Parallel Lines
Proving Lines Parallel
Lines in the Coordinate Plane
Slopes of Parallel and Perpendicular Lines
Constructing Parallel and Perpendicular Lines

D. Congruent Triangles

Congruent Figures
Triangle Congruence by

a) SSS
b) SAS
c) AAS
d) ASA

Isosceles and Equilateral Triangles
Using Corresponding Parts of Congruent Triangles

E. Relationships Within Triangles

Midsegments and Bisectors
Concurrent Lines, Medians, and Altitudes
Inverse, Contrapositives, and Indirect Reasoning
Inequalities in Triangles

F. Quadrilaterals

Properties of Parallelograms
Trapezoids and Kites
Placing Figures in the Coordinate Plane
Proofs Using Coordinate Geometry

G. Area

Parallelograms and Triangles
Pythagorean Theorem and its Converse
Trapezoids, Rhombuses, and Kites
Circles and Arcs
Geometric Probability

H. Similarity

Ratios and Proportions
Proving Triangles Similar
Proportions in Triangles
Perimeters and Areas

I. Right Triangles Trigonometry

Tangent Ratio
Sine and Cosine Ratios
Angles of Elevation and Depression
Vectors

J. Surface Area and Volume

Space Figures, Nets, and Drawings
Pyramids, Cones, Prisms, and Cylinders
Areas and Volumes of Similar Solids

K. Circles

Tangent Lines
Chords and Arcs
Angle Measures and Segment Lengths
Circles in the Coordinate Plane

L.Transformations

Reflections
Translations
Rotations
Symmetry
Tessellations