COURSE TITLE: Geometry
COURSE DESCRIPTION: Geometry provides the vocabulary and skills needed to understand and organize geometrical concepts. It involves students in a deductive system of thought that involves points, lines, angles polygons and polyhedrons. This course emphasizes proof and the applications of algebra to geometry. This is a college preparatory course.
Prerequisite: A minimum grade of "C" in Algebra I or completion of Algebra Part II with Math Department recommendation.
COURSE REQUIREMENTS/REQUIRED MATERIALS:
1. Text: Geometry: Integration, Applications, Connections
Boyd, Burrill, Cummins, Kanold, Malloy
copyright 2001 by Glencoe Division of McGraw-Hill.
2. Pencils.
3. Spiral notebook.
4. Scientific calculator.(TI 83 plus recommended)
COURSE OBJECTIVES/STUDENT OUTCOMES:
1) Students will become familiar with the language of geometry.
Upon completing this goal, the student will be able to
* graph ordered pairs on a coordinate plane
* identify collinear and coplanar points and intersecting lines and
planes
* find the distance between points on a number line, find the distance
between points in the coordinate plane
* find the midpoint of a segment
* identify angles and parts of angles
* classify angles as acute, obtuse, right and straight
* identify and use adjacent angles, vertical angles, complementary
angles, supplementary angles, and linear pairs of angles.
2) Students will experience the elements of deductive reasoning.
Upon completing this goal the student will be able to:
* identify the hypothesis and conclusion of an if-then statement
* write the converse of an if-then statement
* identify and use basic postulates about points, lines, and planes
* use the laws of deductive reasoning
* properly write a proof
3) Students will develop an understanding of the relationship between
angles formed by a transversal intersecting parallel lines.
Upon completing this goal the student will be able to:
* identify the relationships between pairs of angles formed by pairs of
lines and transversals
* recognize angle conditions that produce parallel lines
* prove two lines are parallel based on given angle relationships
* find the slope of a line
* use slope to identify parallel and perpendicular lines
4) Students will acquire an understanding of congruent triangles
and their corresponding parts.
Upon completing this goal the student will be able to:
* identify the parts of a triangle
* classify triangles
* identify congruent triangles
* name and label corresponding parts of congruent triangles
* use postulates SSS, etc. to test for triangle congruence
5) Students will recognize the applications of congruent triangles.
Upon completing this goal the student will be able to:
* identify and use medians, altitudes, angle bisectors and
perpendicular bisectors in a triangle
* recognize and apply relationships between the sides and angles in a
triangle
6) Students will gain an understanding of the properties of
quadrilaterals and the relationship that exists between
quadrilaterals.
Upon completing this goal the student will be able to:
* recognize and define a parallelogram
* use the properties of a parallelogram
* recognize and define a rectangle
* use the properties of a rectangle
* recognize and define the properties of squares and rhombi
* use the properties of squares and rhombi
* recognize and define the properties of trapezoids
* use the properties of trapezoids
7) Students will develop a familiarity with the properties and
applications of similarity.
Upon completing this goal the student will be able to:
* recognize and use ratios and proportions
* identify similar figures
* solve problems involving similar figures
8) Students will experience an introduction to right
triangle trigonometry.
Upon completing this goal the student will be able to:
* find the geometric mean between two numbers
* use the Pythagorean theorem
* recognize and use trigonometric relationships from right triangles
* solve triangles using the law of sines and the law of cosines
9) Students will gain familiarity with the properties of a circle and the
relationship of circles to special lines, i.e. chords, secants, tangents.
Upon completing this goal the student will be able to:
* name parts of a circle
* write an equation of a circle in the plane
* recognize major and minor arcs of circles
* find the measures of arcs and central angles
* find the measures of inscribed angles
* find the measures of angles formed by intersecting chords, secants
and tangents in relation to intercepted arcs
* find the measures of segments formed by intersecting chords,
secants and tangents in relation to intercepted arcs
10) Students will develop a conceptual understanding of the
area of a plane figure.
Upon completing this goal the student will be able to:
* identify and name polygons
* identify faces, edges and vertices of a polyhedron
* find the sum of the measures of the interior and exterior angles of
a convex polygon
* find the measure of each interior and exterior angle of a regular
polygon
* find the area of all standard quadrilaterals
* find the area of regular polygons
* find the area of a circle
11) Students will acquire an understanding of the surface area and
volume of three dimensional figures
Upon completing this goal the student will be able to:
* draw three dimensional figures
* identify the parts of prisms and cylinders
* find the volumes and surface area of standard three dimensional
objects: cylinders, prisms, pyramids, cones, and spheres
12) Students will gain the skills to successfully create geometric
constructions by the use of computer software.
Upon completing this goal the student will be able to:
*draw and label constructions
*measure segment lengths and angle measures
*calculate the areas of polygons
*perform translations, reflections, and rotations
*recognize properties of geometric figures that are not otherwise
immediately obvious
COURSE OUTLINE:
A. The Language of Geometry
1) The coordinate plane
2) Points, lines, planes
3) Problem-solving strategies
4) The measure of a segment
5) Segment relationships
6) Rays and angles
7) Classifying angles
8) Pairs of angles
B. Reasoning and Introduction to Proofs
1) Inductive reasoning and conjecturing
2) If-then statements, converses
3) Deductive reasoning
4) Properties from algebra
5) Problem-solving strategies
6) Two column proofs with segments
7) Two column proofs with angles
C. Parallels
1) Problem solving strategies
2) Parallels and transversals
3) Using parallel lines
4) Proving lines parallel
5) Slopes and lines
6) Parallels and distance
D. Congruent triangles
1) Classifying triangles
2) Angle measure in triangles
3) Congruent triangles
4) Tests for congruent triangles
5) Another test for congruent triangles
6) Problem solving strategies
7) Isosceles triangles
E. Applying Congruent Triangles
1) Special segments in triangles
2) Right triangles
3) Problem solving strategies
4) Indirect proof and inequalities
5) Inequalities for sides and angles of a triangle
6) The triangle inequality
7) Inequalities involving two triangles
F. Quadrilaterals
1) Parallelograms
2) Problem solving strategies
3) Tests for parallelograms
4) Rectangles
5) Squares and rhombi
6) Trapezoids
G. Similarity
1) Properties of proportions
2) Applications of proportions
3) Similar polygons
4) Similar triangles
5) Proportional parts
6) Parts of similar triangles
7) Problem solving strategies
H. Right Triangles and Trigonometry
1) The geometric mean
2) The Pythagorean theorem
3) Special right triangles
4) Trigonometry
5) Applications: using trigonometry
6) Law of sines
7) Law of cosines
8) Problem solving strategies
I. Circles
1) Parts of circles
2) Angles and arcs
3) Arcs and chords
4) Inscribed angles
5) Tangents
6) More angle measure
7) Special segments in a circle
8) Problem solving strategies
J. Polygons and Areas
1) Polygons and polyhedra
2) Angles of Polygons
3) Problem solving strategies
4) Area of Parallelograms
5) Area of triangles, rhombi, and trapezoids
6) Area of regular polygons
7) Area and circumference of a circle
8) Geometric probability
9) Polygons as networks
K. Surface Area and Volume
1) Problems solving strategies
2) Exploring surface area
3) Surface area of prisms and cylinders
4) Surface area of pyramids and cones
5) Volume of prisms and cylinders
6) Volume of pyramids and cones
7) Surface area and volume of spheres
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