Download Essentials of Geometry - Piscataway High School

Essentials of Geometry
Textbook: Geometry Larson
Teachers: Mrs. Gibb & Ms. Bruno
Email: [email protected]
[email protected]
Room: C102
Course description:
Prerequisite: None
This course is designed as a course in a program for students studying college preparatory
mathematics. Initially, the language of Geometry is introduced so that terminology is understood and
infused throughout the class. In addition, students will study the concept of congruency and similarity,
properties of geometric shapes, measurement of plane and solid figures. The concept of proof will be
introduced and vary in depth throughout the course.
Materials:
• 3-ringed Binder with Filler Paper and section dividers
• Writing Instrument (preferably pencils)
• Colored Pencils OR Colored Pens
• Ruler
• Scientific Calculator
Classroom Policies:
Respect is required at all times; not only to the teacher and the classroom, but more importantly
to the student's own learning. To be respectful, students are expected to arrive to class on time, prepared,
and ready to learn and participate. This means that when the period starts, students are seated and ready
to begin with all materials. Assignments are considered part of the necessary materials and are expected
to be submitted on time (late work will be penalized). Visits to the bathroom or lockers should be
addressed before class. Questions are always welcomed!
Lateness, cutting, and absenteeism will be dealt according to school policies. Students have the
number of days he or she was absent to make up work (for example, if you are absent Wednesday, any
work due Wednesday and Thursday will be due Friday without penalty). Students are responsible for
the work they miss. Following missed class time, students should: copy notes from a classmate, ask for
any missed handouts, and if necessary schedule a time to make up in-class work.
Communication is a critical key for success! Students should take every opportunity to ask
questions and come for extra help. Mrs. Gibb is available for extra help Mondays, Wednesdays, and
Thursdays and Ms. Bruno is available for extra help on Mondays and Wednesdays. Extra help is after
school until 3:30pm (if you anticipate coming after school, please let us know)
Grading Policies:
Grading will be on a point system. Tests and projects are usually worth 60-100 points while
quizzes vary in value from 10-40 points. Homework will be checked for completion every day and will
account for about 10 percent of the marking period grade. Quizzes are open notebook and are often
directly related to class notes and/or homework.
Course Schedule: Scope and sequence
Approximate time
frame
Unit 1- The
Language of
Geometry
36 Days
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Chapter 1
Sections 1.1 – 1.6
Chapter 2
Chapter 3
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Congruence and
Transformations
20 Days
Chapter 4
All
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Chapter 9
only 9.6
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Similarity and
Trigonometry
30 Days
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Chapter 6
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Topic
First semester:
Sketch and label simple figures and their intersections
Measure segments and angles
**Add segment lengths and angle measures and use ratios to find
segment lengths and angle measures
**Use midpoint and bisectors to find the length of a segment or angle
measure
Construct and bisect a segment and an angle
Apply the distance and midpoint formulas
**Find the measure of complimentary and supplementary angles and
angles formed by intersecting lines
Find geometric and algebraic patterns and use them to make
predictions (inductive reasoning) and form conclusions by applying
the laws of logic to true statements (deductive reasoning)
Write the converse, inverse, and contrapostive of a conditional
statement in words and in symbols
Write the two conditionals resulting from a biconditional
Understand and find independent, compound and conditional
probabilities
Identify relationships between lines (parallel, perpendicular, skew)
**Identify angles pairs formed by a transversal and find angle
measures if the lines are parallel.
Prove two lines parallel
Find slopes of parallel and perpendicular lines and write equations of
both
Construct parallel and perpendicular lines
Prove Theorems: Vertical Angle Theorem, Alternate Interior Angle
Theorem and Corresponding Angle Theorem
**Find interior and exterior angles of a triangle
Prove the Triangle Sum Theorem
Identify corresponding parts of congruent figures
Identify and prove triangles congruent, including overlapping triangles
and CPCTC
Use isometries to transform figures and explain how they yield
congruent figures, include composition of isometries
Explain how a figure was transformed
Draw and identify lines of symmetry and describe rotational symmetry
Use proportions to solve geometric problems, including geometric
mean
**Find the missing measurement in similar figures and apply
similarity to real-world situations
Prove polygons similar
All
Chapter 9
only 9.7
Chapter 7
All
*** Trigonometry
will be partially
taught in the first
semester but will not
be tested on the
midterm***
Similarity and
Trigonometry
30 Days (Con’t)
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Use proportionality to determine segment lengths in triangles
Perform dilations given a center an scale factor
Prove the Pythagorean Theorem, the Triangle Proportionality
Theorem and its converse.
Classify triangles by angles using side lengths
Use Trig ratios, the Pythagorean Theorem and special right triangles
to solve right triangles in applied problems (include angle of elevation
and depression) and determine the most efficient and accurate method.
**Use geometric mean to solve problems involving similar right
triangles
Second semester:
Use Trig ratios, the Pythagorean Theorem and special right triangles
to solve right triangles in applied problems (include angle of elevation
and depression) and determine the most efficient and accurate method.
*** Trigonometry
will be partially
taught in the first
semester but will not
be tested on the
midterm***
Properties of
Geometric Figures
34 Days
Chapter 5
5.1 – 5.5
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Chapter 8
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Chapter 10
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Identify and find lengths of medians and altitudes of triangles
Prove the Midsegment Theorem and the medians of a triangle meet at
a point
Relate side lengths and angle measures using the triangle inequalities
**Find and use angle measures and side lengths in polygons
Us the hierarchy of quadrilaterals to describe subsets
Determine the type of quadrilateral based on criteria
**Apply properties of special quadrilaterals to find sides and angles
Prove theorems about parallelograms and prove the type of special
quadrilateral on a coordinate plane
**Identify segments and lines related to circles and their properties to
find angle measurements and segment lengths
Find the lengths and measures of arcs
Construct the inscribed and circumscribed circles of a triangle
Derive and graph the equation of a circle given the center and radius
and prove that a given point is located on a circle
Prove that all circles are similar and properties of angles for a
quadrilateral inscribed in a circle
Prove the Perpendicular Bisector Theorem
Measurement
34 Days
Chapter 11
Chapter 12
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Compute perimeters and areas of polygons, including triangles,
rectangles, parallelograms, trapezoids, rhombuses, kites both on and
off the coordinate plane
Find arc length and area of a sector and derive the formulas for each
Construct a regular hexagon and find the area of regular polygons
using properties of special right triangles and trig ratios
Determine the connection between and find the perimeters, area and
volume of similar figures
Determine the geometric probability using segment lengths and
shaded areas
Derive Euler’s Formula using the number of faces, edges and vertices
of a polyhedron
Identify cross-sections of three-dimensional objects and the threedimensional figures formed once a two dimensional figure has been
rotated
Derive surface area and volume formulas and use them to solve
problems, including composite figures
Find all possible dimensions for a given surface area or volume and
determine the maximum or minimum surface area or volume from
given dimensions.