Download Geometry - Salesianum School

GEOMETRY - 423
2008 – 2009
Instructor: Mrs. Katie Godfrey
(302)654-2495 x 201
[email protected]
Course Description
Phase 3
1credit/full year
Grade 9, 10
Students will study postulates and theorems from Euclidean geometry, both from a theoretical and, when
practical, an applied sense. Topics covered include the undefined terms, logic, triangles, triangle congruence
and similarity, quadrilaterals and other polygons, parallelograms, inequalities, right triangles, basic
trigonometry, circles, areas, volumes, and triangle constructions using a straightedge and a compass. Proofs
are also presented in each topic as a logical connection between observation and conclusion. Upon
completion of the course, the student should have a thorough working knowledge of the importance and
beauty of Euclid’s Geometry, as well as a stronger logical base that can be carried into later math courses.
Text
Geometry
Ray Jurgenson, Richard Brown, John Jurgenson
Houghton Mifflin Company, 1994
Assignments
Students will be assigned problems of varying difficulty – from the type “A” and “B” and some “C”
exercises.
Syllabus
First Quarter
Chapter 1: Points, Lines, Planes, and Angles
Chapter 2: Deductive Reasoning
Chapter 3: Parallel Lines and Planes
Second Quarter
Chapter 4: Congruent Triangles
Chapter 5: Quadrilaterals
Chapter 6: Inequalities
Third Quarter
Chapter 7: Similar Polygons
Chapter 8: Right Triangles
Chapter 9: Circles
Fourth Quarter
Chapter 11: Areas of Plane Figures
Chapter 12: Areas and Volumes of Solids
Chapter 13: Coordinate Geometry
Final Exam
The final examination will be composed by the teacher and include questions based on the course objectives
listed below as well as questions that reflect those seen in the SATs.
Grading Policy
To calculate your quarter grade, simply divide the number of points you have earned by the total number of
points that you could have earned at that time in the quarter. Look at the resulting number:
A
100-92.5
B+
92-88.5
B
88-84.5
C+
84-80.5
C
80-76.5
D+
76-72.5
D
72-69.5
F
69-0
Your quarterly grade will be comprised of the following components:
√ GAMEDAY – Your tests will generally be free response and partial credit is awarded so it
is best to show your work. There will be an end of year project assessment as well as an
SAT oriented final year assessment.
√ SCRIMMAGES – Quizzes will also be free response, but can be unannounced.
√ PRACTICES – This includes class work, laboratories, and homework assignments. I will
check your homework each time it is assigned. For every three homeworks not completed a
student’s grade level will drop. It is always best to complete all assignments.
√ PARTICIPATION/SPORTSMANSHIP - Asking and answering questions during class
will be noted. Board work and group work will also be taken into account. This is based on
focus, pride of work, ability to work with others, being prepared, and contributing to
discussions.
√ EXTRA POINT - I will have extra problems or projects available for all students.
Classroom Policy
 During tests and quizzes I will only clarify the directions, unless there is an error on the
test paper.
 Make up policy: All tests and quizzes must be made up 48 hours upon your return
from an absence (barring exceptional circumstances). After that, a grade of zero will be
issued for any missing work.
 If school is canceled (due to snow, etc.), whatever was planned on the canceled day will
be done on the day we come back (tests, quizzes, homework, etc.).
 Your work in this class is your personal property. Academic integrity is the expectation
of every Salesianum student. Any student who jeopardizes this by plagiarism, cheating, or
taking another’s work will receive a zero for the assignment in question. He will also
receive a demerit and parents will be informed.
 Only students with a note from Mrs. Gardner may receive extended time on tests.
 You must tell me each time you wish to use extended time on a test. I must know before
you begin. If you do not tell me before you begin the test, you may not use it on that test.
 If you choose to use extended time, you must finish the test after school the same day.
 To obtain information for the class please use my website found through the Salesianum
website in the Faculty Directory link. Homework assignments and projects will be posted
on my website. FAWeb/Netclassroom will be updated weekly with grades and upcoming
tests/quizzes.
 If a student fails Geometry he will need to make up the credit through an outside summer
course or through a private tutor. The student will also be ineligible for school activities
including athletics. A student must have a passing grade of D or above to move on to
Algebra 2.
Course Objectives
On completion of this course, the student should be able to:
1.
Use the undefined terms: points, line, and plane.
2.
Use terms collinear, coplanar, intersection, and equidistant.
3.
Name angles and find their measures.
4.
Recognize what you can conclude from a diagram.
5.
Recognize the hypothesis and the conclusion of an “if – then” statement.
6.
State the converse of an “if –then” statement.
7.
Use properties from algebra in proofs.
8.
Use the Midpoint Theorem and Angle Bisector Theorem.
9.
Apply the definitions of complementary and supplementary angles.
10. Use the theorem about vertical angles.
11. Apply the definitions and theorems about perpendicular lines.
12. Apply the theorems about supplementary and complementary angles.
13. Plan Proofs then write them in two column proof form.
14. Distinguish between intersecting lines and parallel lines, and skew lines.
15. Apply the theorem about the intersection of the parallel planes by a third plane.
16. Identify the angles formed when two lines are cut by a transversal.
17. Apply the postulates and theorems about parallel lines.
18. Classify triangles according to sides and to angles.
19. Apply the theorem and corollaries about the sum of the measures of the angles of a triangle.
20. Apply the theorem about the measure of an exterior angle of a triangle.
21. Recognize and name convex polygons and regular polygons.
22. Understand and use inductive reasoning.
23. Identify the corresponding parts of a congruent figure.
24. Prove two triangles congruent by using the SSS, SAS, and ASA postulates.
25. Deduce information about segments and angles after proving that two triangles are congruent.
26. Apply the theorems and corollaries about isosceles triangles.
27. Use the AAS and HL postulates to prove triangles congruent.
28. Prove that two overlapping triangles are congruent.
29. Apply the definitions of the median and altitude of a triangle and the perpendicular bisector of a segment.
30. Apply the definition of a parallelogram and the theorems about properties of a parallelogram.
31. Prove that certain quadrilaterals are parallelograms.
32. Apply theorems about parallel lines and the segment that joins the midpoints of two sides of a triangle.
33. Apply the definitions and identify the special properties of a rectangle, rhombus, and square.
34. Apply the definitions and identify the properties of a trapezoid and an isosceles trapezoid.
35. Apply properties of inequality to positive numbers, lengths of segments, and measures of angles.
36. State the contra positive and inverse of an “if – then” statement.
37. Understand the relationship between logically equivalent statements.
38. Draw correct conclusions from given statements.
39. Write indirect proofs in paragraph form.
40. Apply the inequality theorems and corollaries for one triangle and for two triangles.
41. Express a ratio in simplest form.
42. Solve for an unknown term in a given proportion.
43. Express a given proportion in an equivalent form.
44. Apply the properties of similar polygons.
45. Use the AA Similarity Postulate, and the SAS and SSS Similarity Theorem to prove triangles similar.
46. Apply the triangle Angle-Bisector Theorem.
47. Use similar triangles to deduce information about segments.
48. Apply the Triangle Proportionality Theorem and its corollary.
49. Determine the geometric mean between two numbers.
50. Apply the relationships that exist when the altitude is drawn to the hypotenuse of a right triangle.
51. Apply the Pythagorean Theorem and its converse to problems dealing with plane and solid figures.
52. Solve problems using the 30-60-90 and 45-45-90 triangle relationship.
53. Define sine, cosine, and tangent rations for an acute angle.
54. Solve right triangle problems by correct selection and use of the sine, cosine, and tangent ratios.
55. Define and apply the terms circle, sphere, and related parts: diameter, radius, arc, chord, tangent, secant,
segment, and sector.
56. Solve problems involving inscribed angles; angle formed by chords, secants, and tangents; involving lengths of
chords, secant segments, and tangent segments.
57. Make simple constructions with compass and straightedge.
58. Find areas and perimeters of triangles, trapezoids, parallelograms, rectangles, squares, circles, and regular
hexagons and octagons.
59. Find lateral areas, volumes, and total areas of: right prisms, cylinders, and cones; regular pyramids.
60. Apply the properties of similar solids.