GEOMETRY
This class is an introduction to Euclidian geometry. It is meant to be
taken after Algebra 1.
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Students will develop an appreciation of the need for using facts and not just visual
information to classify and prove conjectures.
Students will study basic shapes and how these and other things can be classified.
Students will learn how to use the distance and midpoint formulas
Students will be refreshed in the use of coordinate and noncoordinate geometry
Students will be shown the use of rotational and linear symmetry
Students will look at patterns both geometrical and algebraic
Students will be shown the structure of geometry, being introduced to definitions, postulates,
theorems, and axioms
Students will study segment and angle relationships
Students will look at the structure and how to write converse statements
Students will work with properties from algebra
Students will use deductive reasoning to solve problems
Students will explore lines and planes
Students will look at the connections to algebra
o Slope
o Parallel and perpendicular lines
o How to write simple equations modeling the above
Student will study the use of inverse and contrapositive statements
Students will look at the properties of parallel lines and involve proving things about them
Students will study some of the basics of vectors
o Simple notation
o Length
o Adding vectors
o Doing the dot product
Students will study the basic definitions and structure of triangles
Students will be given information about angles
Students will look at information on isosceles and right triangles
Students will learn all the difference methods of proving triangles congruent
Students will gain knowledge of the special segments and their corresponding points
Students will learn about midsegments
Students will work with inequalities in one and two triangles
Students will study the basic information about various polygons
Students will learn to calculate the size of angles in a polygon
Students will learn to specialize between various quadrilaterals including
o Parallelograms
o Rectangles
o Rhombus
o Squares
o Trapezoids
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o Kites
Students will be shown the congruence methods for polygons
Students will study more about symmetry and specialize in various transformations
Translations
Rotations
Reflections
Glide reflections
Students will study frieze patterns and how the above transformations can make patterns
Students will gain knowledge about similarity
Students will do work with ratios and proportions as they relate to geometry and geometric
figures
Students will work with similar triangles and other polygons
Students will work with dilations and perspective drawings
Students will explore and define right triangles
Students will use the Pythagorean Theorem to both find sides and prove triangles are right
Students will study special right triangles
o 45-45-90
o 30-60-90
Students will study trig ratios as they relate to right triangles
o Sin
o Cos
o Tan
Student will explore and define circles
Students will learn and prove information about
o Tangents
o Central angles and arcs
o Chords
o Inscribe angles
o Other angles formed by a circle and tangents, secants and chords
o Equations of a circle
Students will determine and understand the difference between area and perimeter
Students will use formulas to find the area and perimeter of of
o Triangles
o Squares
o Rectangles
o Rhombuses
o Trapezoids
o Kites
o Circles (arc length and sector area included)
o Areas of similar polygons
Students will study three dimensional figures
Students will do surface area and volumes of
o Cylinders
o Prisms
o Cones
o Pyramids
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o Spheres
Students may study loci both in a plane and in space
MULTICULTURALISM – Students will do multicultural worksheets as they relate to the
material
WRITING – Students will be asked to define various geometric terms and ideas on tests and
quizzes
As it relates, students will do various problems solving activities which also involve the
concepts of geometric proofs.