Download COURSE TITLE: Geometry

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, Burrill, Cummins, Kanold, Yunker, Copyright
1993
by Glencoe Division of Macmillan/McGraw-Hill.
copyrighted
by Merill Publishing Co.
2. Pencils.
3. Spiral notebook.
4. Scientific calculator.(TI 83 plus recommended)
Originally
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 intersection parallel line.
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
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)
4)
5)
6)
7)
Deductive reasoning
Properties from algebra
Problem-solving strategies
Two column proofs with segments
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
1)
2)
3)
4)
5)
6)
7)
Triangles and Trigonometry
The geometric mean
The Pythagorean theorem
Special right triangles
Trigonometry
Applications: using trigonometry
Law of sines
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