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CAHS
Course Outline
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Current Catalog Course Title: Geometry
Course Credit(s): 1
Current Catalog Description :
This course is a study of Euclidean Geometry emphasizing inductive and deductive
reasoning. Students are expected to apply the principals of logic in the solution of formal
proofs. The course will help students develop their abilities to think deductively; to use
an analytic approach in problem solving; to visualize plane and space figures and to
understand relationships between points, lines, planes, and three dimensional figures.
Topics include: points, lines and planes, parallel lines and planes, congruent and similar
polygons, right angles, circles, area and volumes of planes and solid figures, and
coordinate geometry if time permits.
**Algebra I required.
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Instructor Name(s): Ms. Lynne Roy
Instructor E-Mail Address:
[email protected]
Geometry
Course Objectives:
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Identify and model points, lines and planes.
Identify collinear and coplanar points an dintersecting lines and planes in space.
Measure segments and determine accuracy of measurement.
Compute with measures
Find the distance between two points.
Find the midpoint of a segment.
Measure and classigy angles.
Identify and use congruent angles and the bisector of an angle.
Identify and use special pairs of angles.
Identify perpendicular lines
Identify and name polygons.
Find perimeters of polygons.
Make conjectures based on inductive reasoning.
Find counterexamples
Determine truth values of conjunctions and disjunctions
Construct truth tables.
Analyze statements in if-then form.
Write converse, inverse, and contrapositive of if-then statements.
Use the Law of Detachment
Use the Law of Syllogism
Identify and use basic postulates about points, lines, and planes.
Write paragraph proofs
Use algebra to write two column proofs.
Use properties of equality in geometry proofs
Write proofs involving segment addition
Write proofs involving segment congruence
Write proofs involving supplementary and complementary angles
Write proofs involving congruent and right angles.
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Identify the relationships between two lines or two planes
Name angles formed by a pair of lines and a transversal
Use the properties of parallel lines to determine congruent angles
Use algebra to find angle measures
Find slopes of lines
Use slope to identify parallel and perpendicular lines
Write an equation of a line given information
Recognize angle conditions that occur with parallel lines
Prove that two lines are parallel based on given angle relationships
Find the distance between a point and a line
Find the distance between parallel lines
Identify and classify triangles by angles.
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Identify and classigy triangles by sides
Apply the angle sum theorem
Apply the exterior angle theorem
Name and label corresponding parts of congruent triangles
Identify congruence transformations
Use the SSS postulate to test for triangle congruence
Use the SAS postulate to test for triangle congruence
Use the ASA postulate to test for triangle congruence
Use the AAS theorem to test for triangle congruence
Use properties of isosceles triangles
Use properties of equilateral triangles
Identify and use perpendicular bisectors and angle bisectors in triangles.
Identify and use medians and altitudes in triangles
Recognize and apply properties of inequalities to the measures of angles of a trianlge
Recognize and apply properties of inequalities to the relationships between angles and
sides of a triangle.
Apply the Triangle Inequality Theorem
Determine the shortest distance between a point and a line.
Write ratios
Use properties of proportions
Identify similar figures
Solve problems involving scale factors
Identify similar triangles
Use similar triangles to solve problems
Use proportional parts of triangles
Divide a segment into parts
Recognize and use proportional relationships of corresponding perimeters of similar
triangles
Recognize and use proportional relationships of corresponding angle bisectors, altitudes,
and medians of similar triangles
Find the geometric mean between two numbers.
Solve problems involving relationships between parts of a right triangle and the altitude to
its hypotenuse
Use the Pythagorean Theorem
Use the converse of the Pythagorean Theorem
Use properties 45-45-90 triangles
Use properties 30-60-90 triangles
Find trigonometric ratios using right triangles
Solve problems using trigonometric ratios
Solve problems involving angles of elevation
Solve problems involving angles of depression
Find the sum of the measures of the interior angles of a polygon
Find the sum of the measures of the exterior angles of a polygon
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Recognize and apply properties of the sides and angles of parallelograms
Recognize and apply properties of the diagonals of parallelograms
Recognize the conditions that ensure a quadrilateral is a parallelogram
Prove that a set of points forms a parallelogram in the coordinate plane.
Recognize and apply properties of rectangles
Determine whether parallelograms are rectangles
Recognize and apply the properties of rhombi
Recognize and apply the properties of squares
Recognize and apply the properties of trapezoid
Solve problems involving the medians of trapezoids.
Identify and use parts of circles
Solve problems involving the circumference of a circle
Recognize major arcs, minor arcs, semicircles, and central angles and their measures
Find arc length
Recognize and use relationships between arcs and chords
Recognize and use relationships between chords and diameters
Find measures of inscribed angles
Finde measures of angles of inscribed polygons
Use properties of tangents
Solve problems involving circumscribed polygons
Find measures of angles formed by lines intersecting on or in side a circle
Find measures of angles formed by lines intersecting outside the circle
Find measures of segments that intersect in the interior of a circle
Find measures of segments that intersect in the exterior of a circle
Find perimeters and areas of parallelograms
Determine whether points on a coordinate plane define a parallelogram
Find areas of triangles
Find areas of trapezoids and rhombi
Find areas of regular polygons
Find areas of circles
Find areas of irregular figures
Find areas of irregular figures on the coordinate plane
Solve problems involving geometric probability
Solve problems involving sectors and segments of circles
Use orthogonal drawings of three-dimensional figures to make models
Identify and use three-dimensional figures
Draw two-dimensional models for three-dimensional figures
Find surface area
Find lateral areas of prisms
Find surface areas of prisms
Find lateral areas of cylinders
Find surface areas of cylinders
Find lateral areas of regular pyramids
Find surface areas of regular pyramids
Find lateral area of cones
Find surface areas of cones
Recognize and define basic properties of spheres
Find surface areas of spheres
Find volumes of prisms
Find volumes of cylinders
Find volumes of pyramids
Find voumes of circular cones
Find volumes of spheres
Solve problems involving volumes of spheres
1. Teaching Methods:
o Lecture, demonstration, group work
2. Materials and Resources:
Required Text(s): Glencoe Geometry
Required Materials: sharpened pencil / pen, notebook, calculator (scientific or
graphing), book
Tutoring is available Monday thru Thursday from 2:30pm – 4:00 pm. Morning
sessions are available by appointment.
3. Evaluation:
o Homework
o Graded assignments
o Quizzes
o Tests
o In class projects / assignments
4. Other Policies and Procedures:
Expectations:
o Have your pencil sharpened and calculator picked up before class begins.
o When the bell rings you should be prepared to begin class: ie- book open,
homework out, etc. Tardiness will not be accepted
o Complete your homework daily
o Usage of the restroom is at the beginning or end of class (not the middle!!).
You must have your pass book to go to the restroom.
Respect:
o Show respect to myself or my substitute at all times and you will receive the
same.
o Respect yourself and others, asking questions and making mistakes is part of
our nature.
o Do not disrupt others via talking or interrupting. This will result in
disciplinary action.
Requirements:
o Notebook- daily notes, classroom examples, homework.
o Show all work- I can’t tell you what you did wrong unless I can see what you
did.
o Absences- it is your responsibility to get any work missed, complete it, and
turn it in. If you fail to do so, the missed work will be counted as a ZERO!
You are given one day for every day missed to make up that work.
5. Instructor Name (s): Lynne Roy
6. Course Plan:
GeometryI:
1. Chapter 1 – Points, Lines, Planes and Angles
o 1.1- Points, Lines, and Planes
o 1.2- Linear Measure and Precision
o 1.3- Distance and Midpoints
o 1.4- Angle Measure
o 1.5- Angle Relationships
o 1.6- Polygons
2. Chapter 2 – Reasoning and Proof
o 2.1- Inductive Reasoning and Conjecture
o 2.2- Logic
o 2.3- Conditional Statements
o 2.4- Deductive Reasoning
o 2.5- Postulates and Paragraph Proofs
o 2.6- Algebraic Proof
o 2.7- Proving Segment Relationships
o 2.8- Proving Angle Relationships
3. Chapter 3 – Parallel and Perpendicular Lines
o 3.1- Parallel lines and transversals
o 3.2- Angles and Parallel lines
o 3.3- Slopes of Lines
o 3.4- Equations of lines
o 3.5- Proving lines parallel
4. Chapter 4 – Congruent Triangles
o 4.1,4.2 – Classifying triangles and angles of triangles
o 4.3 – Congruent triangles
o 4.4- Proving congruence – SSS, SAS
o 4.5- Proving Congruence – ASA, AAS
o 4.6- Isosceles Triangles
5. Chapter 5 – Relationships in Triangles
o 5.1- Bisectors, Medians, and Altitudes
o 5.2- Inequalities and Triangles
o 5.4 – The Triangle Inequality
6. Chapter 6 – Proportions and Similarity
o 6.1 – Proportions
o 6.2 – Similar Polygons
o 6.3- Similar Triangles
o 6.4- Parallel lines and proportional parts
o 6.5- Parts of similar triangles
7. Chapter 7 – Right Triangles and Trigonometry
o 7.1- Geometric Mean
o 7.2- The Pythagorean Theorem and its converse
o 7.3 – Special Right triangles
o 7.4- Trigonometry
o 7.5- angles of elevation and depression
8. Chapter 8- Quadrilaterals
o 8.1- Angles of polygons
o 8.2- Parallelograms
o 8.3- Tests for parallelograms
o 8.4- Rectangles
o 8.5- Rhombi and Squares
o 8.6- Trapezoids
9. Chapter 10 – Circles
o 10.1- Circles and circumference
o 10.2- angles and arcs
o 10.3- arcs and chords
o 10.4- Inscribed angles
o 10.5- Tangents
o 10.6- Secants, Tangents and Angle measures
o 10.7- Special segments in a circle
10. Chapter 11- Areas of polygons and circles
o 11.1- Areas of parallelograms
o 11.2- Areas of triangles, trapezoids and rhombi
o 11.3- Areas of Regular polygons and circles
o 11.4- Areas of Irregular figures
o 11.5- Geometric Probability
11. Chapter 12 – Surface Area
o 12.1- Three dimensional figures
o 12.3- Surface areas of prisms
o 12.4- Surface area of cylinders
o 12.5- Surface areas of pyramids
o 12.6- Surface Area of cones
o 12.7- Surface area of spheres
12. Chapter 13 – Volume
o 13.1- Volume of cylinders and prisms
o 13.2- volumes of pyramids and cones
o 13.3- volumes of spheres
7. During the semester/session, reasonable changes to the course outline may be
academically appropriate; however students will be notified of these adjustments
in a timely manner.
Miss Lynne Roy______________
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Instructor Signature
August 25, 2009
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Date