Download Welcome Course: Geometry Teacher: A. Ferraro Contact: AFerraro

Welcome
Course:
Teacher:
Contact:
Geometry
A. Ferraro
[email protected]
Please feel free to contact me anytime via email. I believe it is the best
means of communication. I check my email often throughout the day.
Course Description
The Geometry curriculum has been revised to align with the current New York State
Standards of 2008. It has been designed to improve the problem solving abilities of each student
while continuing to develop mathematical skills, concepts, and computation. Critical thinking,
organizational skills, and the ability to communicate effectively are also stressed throughout the
year. It is intended that each student will obtain a better understanding of the material studied
and attain the knowledge necessary to successfully continue in the high school mathematics
program.
Throughout the school year, students will study the various topics, outlined below,
through the use of individual, partnered and group work. Students will use various materials and
resources in order to fully understand the covered concepts. It is my hope that all students will
have a greater interest and appreciation for mathematics upon completion of this class.
Supplies
 Pencils
 Paper
 3-ring binder
 5 section dividers labeled:
Warm Ups
Notes
HW
Quizzes
Review
Remember: The more organized you are, the easier it will be to
study for homework quizzes, quizzes, cumulative quizzes, and tests.
Homework – 35%
Homework is a critical part of learning mathematics. Mathematics is not a “spectator sport.”
One must do math in order to learn math. It is crucial that students complete all assigned
homework by the beginning of each class. Homework is assigned for practice after each topic
has been discussed in class. If they pay attention in class, students will be able to complete all
respective assignments. Any questions regarding homework will be addressed during homework
review at the beginning of each class. I strongly believe it is a time for practice and learning.
 There are no late homework assignments.
 Every Friday there will be a homework quiz, with the exception of the final
Friday of the month. At the end of each quarter, two of these quiz grades will
be dropped. If you are absent for a homework quiz, it will count as a zero

(that quiz grade can be dropped as one of the two drops). This should
encourage you to ask questions and discourage you from copying homework.
Your overall homework average will be the average of your in class homework
quizzes and your daily homework completion.
Quizzes – 20%
Quizzes are given bi-weekly as a way of monitoring student progress. Cumulative quizzes will
be given at the end of each month. It is our hope that the constant review will help you to feel
more confident and be more prepared for midterms/final exams.
Tests – 45%
Tests will be given at the completion of each unit. Tests will demonstrate students' mastery of
the topics covered.
***Attendance NOTE: If you are absent for a quiz, cumulative quiz or test, you have ONE
WEEK from the date it was given to make it up. If you do not make it up in this time, the
grade will be recorded as a zero.
Course Grade
Since this is a full year course, your course grade is calculated using the following:
Each quarter counts as 2/10 Midterm is 1/10
Final Exam is 1/10
EXTRA HELP
We strongly encourage you to seek extra help when you are struggling or when you do not
understand a concept, however the intent of extra help is not to provide you with an excuse to
pay less attention in class. The purpose of extra help is to assist you in becoming more
independent, not more dependent on us. We do not want to encourage poor habits or enable
you by allowing you to depend on us too much; we want to help you learn how to help
yourself.
Students are expected to be Respectful, Responsible and Prepared
each and every day 
I look forward
successful school year.
can so that you will
potentials. Best wishes
to working with each and every one of you for a very
It is my hope to provide you all with the best opportunities I
have the chance to learn and succeed to your greatest
for a great school year!
~Mrs. Ferraro
In the words of Galileo:
“You can not teach a man (human) anything; you can only help him to
discover it in himself.”
Geometry Curriculum
I. Coordinate Geometry
A. Uses of Slope, Midpoint, and Distance Formulas
1. Lines and Line Segments
i. Find the slope of a perpendicular line, given the equation of a line
ii. Determine whether two lines are parallel, perpendicular, or neither, given their equations
iii. Find the equation of a line, given a point on the line and the equation of a line perpendicular to
the given line
iv. Find the equation of a line, given a point on the line and the equation of a line parallel to the
desired line
v. Find the midpoint of a line segment, given its endpoints
vi. Find the length of a line segment, given its endpoints
vii. Find the equation of a line that is the perpendicular bisector of a line segment, given the
endpoints of the line segment
viii. Solve systems of equations involving one linear equation and one quadratic equation
2. Polygons
i. Investigate, justify, and apply the properties of triangles and quadrilaterals in the coordinate
plane
3.Circles
i. Write the equation of a circle, given its center and radius or given the endpoints of the
diameter
ii. Write the equation of a circle, given its graph
iii. Find the center and radius of a circle, given the equation of the circle in center-radius form.
iv. Graph circles in the form (x – h)2 + (y – k)2 = r2.
II. Transformational Geometry
A. Application of Transformations
1. Define, investigate, justify, and apply isometries in the plane – rotations, reflections, translations, glide
reflections - using function notation
2. Investigate, justify, and apply the properties that remain invariant under translations, rotations,
reflections, and glide reflections.
3. Identify specific isometries by observing orientations, numbers of invariant points, and/or parallelism
4. Justify geometric relationships (perpendicularity, parallelism, congruence) using transformational
techniques
5. Identify specific similarities by observing orientation, number of invariant points, and/or parallelism
6.Investigate, justify, and apply the analytical representations for translations, rotations about the origin of
90 degrees and 180 degrees, reflections over the lines x = 0, y = 0, and y = x, and dilations centered at the
origin
B.Similar Figures
1. Define, investigate, justify, and apply similarities (dilation and the composition of dilations and
isometries)
2. Investigate, justify, and apply the properties that remain invariant under similarities
III. Constructions and Locus
A. Constructions
1. Construct a bisector of a given angle, using a straightedge and compass, and justify the construction
2. Construct the perpendicular bisector of a given segment, using a straightedge and compass, and justify
the construction
3. Construct lines parallel to a given line through a given point, using a straightedge and compass, and
justify the construction
4. Construct lines perpendicular to a given line through a given point, using a straightedge and compass,
and justify the construction
5. Construct an equilateral triangle, using a straightedge and compass, and justify the construction
B. Locus
1. Investigate and apply the concurrence of medians, altitudes, angle bisectors, and perpendicular bisectors
of triangles
2. Solve problems using compound loci
3. Graph and solve compound loci in the coordinate plane
IV. Three-Dimensional Objects
A. Prism
1. the lateral edges of a prism are congruent and parallel
2. two prisms have equal volumes if their bases have equal areas and their altitudes are equal in length
3. The volume of a prism is the product of the area of the base and the altitude.
B. Regular Pyramid
1. Properties
i. Lateral edges are congruent
ii. Lateral faces are congruent isosceles triangles
iii. Volume of a pyramid equals one-third the product of the area of the base and the altitude
C. Cylinder
1. Properties
i. Bases are congruent
ii. Volume equals the product of the area of the base and the altitude
iii. Lateral area of a right cylinder equals the product of an altitude and the circumference of the
base
D. Right Circular Cone
1. Properties
i. Lateral area equals one-half the product of the slant height and the circumference of its base.
ii.Volume is one-third the product of the area of its base and its altitude
E. Sphere
1. The intersection of a plane and a sphere is a circle
2. A great circle is the largest circle that can be drawn on a sphere
3. Two planes equidistant from the center of the sphere and intersecting the sphere do so in congruent
circles
4. Surface area is 4ðr2
5. Volume is (4/3)(pi)r3
I. Logic
1. Determine the negation of a statement and establish its truth value
2. Know and apply the conditions under which a compound statement is true
A. Conjunction
B. Disjunction
C. Conditional
D. Biconditional
3. Identify and write the inverse, converse, and contrapositive of a given conditional statement and note the
logical equivalences
4. Write a proof arguing from a given hypothesis to a given conclusion
II. Euclidean Geometry and Proofs
1. Definitions, Theorems, Postulates, and Properties
a. If a line is perpendicular to each of two intersecting lines at their point of intersection, then the
line is perpendicular to the plane determined by them.
b. Through a given point there passes one and only one plane perpendicular to a given line.
c. Through a given point there passes one and only one line perpendicular to a given plane.
d. Two lines perpendicular to the same plane are coplanar
e. Two planes are perpendicular to each other if and only if one plane contains a line perpendicular
to the second plane.
f. If a line is perpendicular to a plane, then any line perpendicular to the given line at its point of
intersection with the given plane is in the given plane.
g. If a line is perpendicular to a plane, then every plane containing the line is perpendicular to the
given plane.
h. If a plane intersects two parallel planes, then the intersection is two parallel lines.
i. If two planes are perpendicular to the same line, they are parallel.
2. Triangles
a. Determine the congruence of two triangles by using one of the five congruence techniques
(SSS, SAS, ASA, AAS, and HL), given sufficient information about the sides and/or angles of two
congruent triangles.
b. Identify corresponding parts of congruent triangles.
c. Investigate, justify, and apply theorems about the sum of the measures of the angles of a
triangle.
d. Investigate, justify, and apply the isosceles triangle theorem and its converse.
e. Investigate, justify, and apply theorems about geometric inequalities, using the exterior angles
theorem.
f. Investigate, justify, and apply the triangle inequality theorem.
g. Determine either the longest side or a triangle give the three angle measures or the largest angle
given the lengths of three sides of a triangle.
h. Investigate, justify, and apply theorems about geometric relationships, based on the properties
of the line segment joining the midpoints of two sides of the triangle
i. Investigate, justify, and apply theorems about the centroid of a triangle, dividing each median
into segments whose lengths are in the ratio 2:1.
j. Investigate, justify, and apply the Pythagorean Theorem and its converse
3. Parallel Lines
a. Determine if two lines cut by a transversal are parallel, based on the measure of given pairs of
angles formed by the transversal and the lines.
4. Quadrilaterals
a. Investigate, justify, and apply theorems about the sum of the measures of the interior and
exterior angles of polygons.
b. Investigate, justify, and apply theorems about each interior and exterior angle measure of
regular polygons
c. Investigate, justify, and apply theorems about parallelograms involving their angles, sides, and
diagonals.
d. Investigate, justify, and apply theorems about special parallelograms (rectangles, rhombuses,
squares) involving their angles, sides, and diagonals
e. Investigate, justify, and apply theorems about trapezoids (including isosceles trapezoids)
involving their angles, sides, medians, and diagonals.
f. Justify that some quadrilaterals are parallelograms, rhombuses, rectangles, squares, or
trapezoids.
5. Similarity
a. Establish similarity of triangles, using the following theorems: AA, SAS, and SSS.
b. Investigate, justify, and apply theorems about similar triangles.
c. Investigate, justify, and apply theorems about proportional relationships among the segments of
the sides of the triangle, given one or more lines parallel to one side of a triangle and intersecting
the other two sides of the triangle.
d. Investigate, justify, and apply theorems about mean proportionality:
i. the altitude to the hypotenuse of a right triangle is the mean proportional between the
two segments along the hypotenuse
ii. the altitude to the hypotenuse of a right triangle divides the hypotenuse so that either
leg of the right triangle is the mean proportional between the hypotenuse and segment of
the hypotenuse adjacent to that leg
6. Circles
a. Investigate, justify, and apply theorems regarding chords of a circle:
i. perpendicular bisectors of chords
ii. the relative lengths of chords as compared to their distance from the center of the circle
b. Investigate, justify, and apply theorems about tangent lines to a circle:
i. A perpendicular to the tangent at the point of tangency
ii. Two tangents to a circle from the same external point
iii. Common tangents of two-intersecting or tangent circles
c. Investigate, justify, and apply theorems about the arcs determined by the rays of angles formed
by two lines intersecting a circle when the vertex is:
i. inside the circle (two chords)
ii. on the circle (tangent and chord)
iii. outside the circle (two tangents, two secants, or tangent and secant)
d. Investigate, justify, and apply theorems about arcs of a circle cut by two parallel lines
e. Investigate, justify, and apply theorems regarding segments intersected by a circle
i. along two tangents from the same external point
ii. along two secants from the same external point
iii. along a tangent and a secant from the same external point
iv. along two intersecting chords of a given circle