Download Course Outline Geometry(5210)2009

Geometry: Goals and Course Outline
DEPARTMENT: Mathematics
COURSE TITLE: Geometry
o YEAR
o SEMESTER
DATE: 2010-2011
COURSE NUMBER: 5210
QPA: 4.5
CREDITS: 5
TEXTBOOK: (Title, Author, Publisher, Edition)
McDougal Littell Geometry (Both print and electronic editions), Larson, Boswell,
Kanold, & Stiff, McDougal Littell Inc., 2007
MATERIALS USED: TI-84 Plus graphing calculators, IBM ThinkPad, supplementary
materials as supplied by McDougal Littell, protractor and compass
GOALS:
1. To provide a basic comprehensive course in geometry that is very concrete and
visual.
2. To discern patterns and recognize properties of two-dimensional geometric
shapes.
3. To reinforce the fundamentals of algebra in a geometric setting.
4. To prepare students for the Math portions of the SAT.
5. To use visualization, spatial reasoning, and geometric modeling to solve problems.
6. To use graphing calculators and measurement tools to analyze, solve, visualize,
and clarify geometric concepts.
CONTENT OF COURSE:
FIRST SEMESTER
Unit 1: Fundamentals of Geometry
1. Naming points, lines, rays, line segments and planes
2. Segment addition and congruence
3. The midpoint formula and its use to determine the midpoint of a line segment on a
coordinate plane
4. The distance formula and its use to calculate the exact length of a line segment on
a coordinate plane
5. Measuring and classifying angles
6. Angle addition
7. Special angle pair relationships
8. Classifying polygons
Unit 2: Reasoning and Proof
1. Using inductive reasoning to arrive at conjectures about observed events
2. Testing the validity of conjectures
3. Converting factual statements into conditional statements
4. Writing the converse of conditional statements
5. Point, line, and plane postulates
6. Review algebraic properties of equality
7. Right Angle Congruence Theorem
8. Linear Pair Postulate
9. Vertical Angles Congruence Theorem
Unit 3: Parallel and Perpendicular Lines
1. Review the concepts of parallel and perpendicular lines and planes
2. Skew lines
3. Special angle pairs formed when a transversal intersects a pair of lines
4. Measurements of special angle pairs formed when the lines intersected by a
transversal are parallel
5. Review of slopes of lines
6. Review of writing equations in slope-intercept form and point-slope form
7. Review of graphing linear equations
8. Perpendicular transversal theorem
SECOND SEMESTER
Unit 4: Congruent Triangles
1. Classification of triangles by side lengths
2. Use of protractor to determine angle measurement
3. Classification of triangles by angle measurements
4. Triangle Sum Theorem
5. Exterior Angle Theorem
6. Properties of congruent figures
7. Prove triangles are congruent by SSS, SAS, ASA, and AAS
8. Real life applications of triangle congruence
9. Base angle theorem of isosceles triangle
10. Equilateral triangle is also equiangular
11. Perimeter of triangle
12. Congruence transformations
Unit 5: Relationships within Triangles
1. Angle bisectors
2. Medians
3. Altitudes
4. Area of triangles
5. Relationship between side length and angle measurement in a triangle
6. Triangle Inequality Theorem
Unit 6: Similarity
1. Ratios
2. Percent of change
3. Proportions
4. Geometric mean
5. Using proportions to solve problems
6. Similar polygons
Unit 7: Right Triangles
1. Pythagorean Theorem
2. Pythagorean triples
3. Converse of Pythagorean Theorem
Unit 8: Circles
1. Basic definitions: circle, radius, diameter
2. Circumference formula
3. Area formula
4. Area of a sector
Unit 9: Quadrilaterals
1. Characteristics of parallelograms, rectangles, squares, and trapezoids
2. Perimeter
3. Area
4. Shaded area
Geometry Unit Proficiencies
Students will be able to…
Unit 1: Fundamentals of Geometry
1. Identify points, lines, line segments, rays and planes.
2. Symbolically name a point, a line, a line segment, a ray and a plane.
3. Recognize problematic situations that call for segment addition.
4. Demonstrate knowledge of the midpoint formula and competence in inputting
values into the distance formula.
5. Simplify radicals.
6. Determine the midpoint of a line segment on a coordinate plane using the midpoint formula.
7. Calculate the length of a line segment on a coordinate plane using the distance
formula and present result in simplest radical form.
8. Identify segment congruence.
9. Name, measure, and classify angles.
10. Recognize problematic situations that call for angle addition.
11. Identify special angle pairs: complementary, supplementary, linear pair and
vertical angles.
12. Classify polygons.
Unit 2: Reasoning and Proof
1. Use inductive reasoning to form conjectures about observed events.
2. Determine the validity of a conjecture and present a counterexample to demonstrate the falsity of an invalid conjecture.
3. Convert a factual statement into a conditional statement.
4. Identify the hypothesis and conclusion of a conditional statement.
5. Write the converse of a conditional statement.
6. Interpret geometric diagrams by means of point, line, and plane postulates.
7. Appreciate that algebraic properties of equality substantiate all of the steps used to
solve an algebraic equation.
8. Understand that all right angles are congruent.
9. Understand that angles that form a linear pair are supplementary.
10. Understand that vertical angles are congruent.
Unit 3: Parallel and Perpendicular Lines
1. Recognize parallel, perpendicular and skew lines and understand the distinctions
between them.
2. Distinguish between corresponding, alternate interior, alternate exterior, and consecutive interior angles formed when a transversal intersects a pair of lines.
3. Determine the measurements of all eight angles formed when a pair of parallel
lines are intersected by a transversal when only one of the angle measurements is
known.
4.
5.
6.
7.
Determine the slope of a line when viewing its graph.
Calculate the slope of a line algebraically by means of the slope formula.
Write the equation of a line when presented with its graph.
Write the equation of a line in slope-intercept or point-slope form when given its
slope and a point or when given two points.
8. Appreciate that the perpendicular transversal theorem is an extension of angle relationships present when a pair of parallel lines are intersected by a transversal.
Unit 4: Congruent Triangles
1. Distinguish between scalene, isosceles, and equilateral triangles using definitions.
2. Use a protractor to determine the approximate measurement of an angle.
3. Distinguish between acute, right, obtuse, and equiangular triangles.
4. Determine the measurement of a missing angle of a triangle by means of the
Triangle Sum Theorem.
5. Understand how the measurement of an exterior angle of a triangle relates to the
measurements of its interior angles.
6. Identify all pairs of congruent corresponding parts of congruent figures.
7. Determine if figures are congruent.
8. Appreciate that congruent triangles can be used to find distances that are difficult
to measure directly.
9. Determine measurements of all three angles of an isosceles triangle when only one
angle measurement is known.
10. Determine the perimeter of a triangle with the appropriate knowns.
11. Create an image congruent to a given figure in the coordinate plane.
12. Distinguish between the three main types of transformations.
Unit 5: Relationships within Triangles
1. Identify special triangle segments.
2. Understand the properties of points located on angle bisectors.
3. Understand that the altitude of a triangle is referred to as the height of a triangle
and is therefore very important in determining the area of a triangle.
4. Use the triangle area formula to calculate the area of a triangle.
5. Explain how triangle side lengths relate to angle measurements.
6. List the sides of a triangle in order when given its angle measurements and vice
versa.
7. List possible lengths of the third side of a triangle when the lengths of its two other
sides are given.
Unit 6: Similarity
1. Simplify a ratio.
2. Calculate the percent of increase/decrease given original amount and resulting
amount after the increase/decrease.
3. Use ratios to find missing dimensions.
4. Recognize a proportion and use the cross products property to solve it.
5. Recognize when a proportion approach is appropriate for solving real world problems.
6. Calculate the geometric mean of two numbers and present it in simplest radical
form.
7. Identify similar polygons by investigating angle measurements and proportionality of corresponding sides.
8. Determine the scale factor of similar polygons and use it to determine lengths of
missing dimensions.
9. Appreciate that similar polygons also exhibit proportionality of perimeters and internal segment lengths.
Unit 7: Right Triangles
1. Apply the Pythagorean Theorem to determine the length of a missing side of a
right triangle.
2. Recognize common Pythagorean triples and their multiples.
3. Understand that these Pythagorean triples can be put to use to quickly arrive at the
length of a missing side of a right triangle.
4. Use the Pythagorean Theorem to classify a triangle as right, acute, or obtuse.
Unit 8: Circles
1. Define a circle.
2. Distinguish between the radius and diameter of a circle and demonstrate clear
understanding of how these measurements relate to one another.
3. Calculate the exact circumference of a circle when given its radius or diameter.
4. Determine the radius when the circumference is known.
5. Calculate the exact area of a circle when given its radius or diameter.
6. Determine the radius when the area is known.
7. Determine the area of a shaded section of a circle with a central angle of known
measurement.
Unit 9: Quadrilaterals
1. Compare and contrast parallelograms, rectangles, squares, and trapezoids.
2. Determine the perimeter of an quadrilateral.
3. State the area formula for a parallelogram, rectangle, square, and trapezoid.
4. Calculate the area of a parallelogram, rectangle, square, and trapezoid.
5. Find the area of a section of a geometric sketch which is a composite of any of
these quadrilaterals or one of these quadrilaterals and an inscribed or circumscribed circle.