Download ABSE 025 Rev May 2014 - Glendale Community College

Noncredit
Glendale Community College
May 2014
COURSE OUTLINE
Adult Basic and Secondary Education 025
Geometry 1A
I.
Catalog Statement
Adult Basic and Secondary Education 025 is the first half of a one -year high school level
geometry course. In this course the notion of two-dimensional shapes as part of the
Euclidian Plane and exploration of transformations of this plane as a way to determine
whether two shapes are congruent are formalized. Students use transformations to prove
geometric theorems. This course is designed to meet the needs of students who wish to
begin their study of geometry and to earn high school credit in math.
Units: 0.0
Total Laboratory Hours: 100.0
Total Faculty Contact Hours: 100
Recommended preparation: ESL 040 or equivalent, ABSE 024 or equivalent.
Note: This is a self-paced course in an open-entry, open-exit lab environment. Successful
completion of this course is worth 5 credits (.5 unit) towards a high school diploma.
II.
Course Entry Expectations
Skills Level Ranges: Reading: 5; Writing: 4; Listening/Speaking: 4; and Math: 4.
III.
Course Exit Standards
Upon successful completion of the required coursework, the student will be able to:
1. make a variety of formal geometric constructions using a variety of tools;
2. experiment with transformations in the plane;
3. understand congruence in terms of rigid motions;
4. explain triangle congruence in terms of rigid motion;
5. prove theorems about lines and angles, triangles, and parallelograms.
IV.
Course Content
A. Foundations for Geometry
1. Points, lines, and planes
2. Segment and angle measurement
3. Pairs of angles
4. Formulas in geometry
16 hours
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5. Midpoint and distance formulas
6. Transformations
B. Transformational Geometry
1. Reflections
2. Translations and rotations
3. Compositions of transformations
4. Symmetry
5. Dilations
17 hours
C. Geometric Reasoning
1. Inductive reasoning
2. Conditionals and deductive reasoning
3. Biconditionals and definitions
4. Algebraic proof
5. Geometric proof
14 hours
D. Parallel and Perpendicular Lines
1. Parallel lines
2. Transversals
3. Parallel line theorems
4. Constructions and problem solving
5. Quadrilaterals and parallels
6. Proving lines parallel
18 hours
E. Triangle Congruence
18 hours
1. Properties and angle relationships in triangles
2. Congruent triangles
3. Triangle congruence: side-side-side (SSS), side-angle-side (SAS), angle-side-angle
(ASA), hypotenuse-leg (HL), corresponding parts of congruent triangles are
congruent (CPCTC)
4. Introduction to coordinate proof
5. Isosceles and equilateral triangles
F. Properties and Attributes of Triangles
1. Perpendicular and angle bisectors
2. Bisectors, medians, and altitudes of triangles
3. The triangle midsegment theorem
4. Inequalities in one and two triangle
V.
Methods of Instruction
The following methods of instruction may be used in the course:
1. independent study using worksheets and texts;
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Adult Basic and Secondary Education 025
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2. computer-aided instruction;
3. small group instruction;
4. video instruction.
VI.
Out of Class Assignments
Not Applicable
VII. Methods of Evaluation
The following methods of evaluation may be used in the course:
1. complete the entire individualized contract;
2. assessments at the end of each chapter;
3. unit tests;
4. final exam.
VIII. Textbook(s)
Burger, Edward, et. al. California Geometry. Austin: Holt, Reinhart and Winston,
2008. Print.
10th Grade Textbook Reading Level: ISBN 978-0-03-092345-6
IX.
Student Learning Outcome
Upon Successful completion of the required coursework, the student will be able to:
1. make formal geometric constructions with a variety of tools and methods: copying a
segment, copying an angle, bisections of a segment or of an angle, construction of
the perpendicular bisector of a line segment, and constructing a line parallel to a
given line through a point not on the line;
2. use rigid motion to map corresponding parts of congruent triangles onto each other
and use the criteria for triangle congruence (ASA, SAS, and SSS) to prove triangle
congruence;
3. prove theorems about lines and angles: vertical angles are congruent; when a
transversal crosses parallel lines, alternate interior angles are congruent and
corresponding angles are congruent;
4. prove theorems about triangles: measures of interior angles of a triangle sum to
180; base angles of isosceles triangles are congruent; the segment joining
midpoints of two sides of a triangle is parallel to the third side and half the length;
the medians of a triangle meet at a point;
5. verify experimentally that in a triangle, angles opposite longer sides are larger,
sides opposite larger angles are longer, and the sum of any two sides lengths is
greater than the remaining side length.