Download Geometry Syllabus_30512_1 - Pearson-Global

COURSE OVERVIEW
The geometry course is centered on the beliefs that
The ability to construct a valid argument is the basis of logical communication, in both mathematics
and the real-world.
There is a need to be able to visualize the movement and orientation of two and three-dimensional
figures, to visualize lines and planes in space, and to apply this knowledge to one’s surroundings.
Geometry helps you communicate about the world around you because you can more accurately
describe what you see.
Geometry is best learned when algebra, constructions, measurement, and the coordinate plane are
integrated throughout the course, rather than learning each concept in isolation. In this way, each skill is
built through continued practice and more concepts are related and compared. As a result, students are
more likely to make connections and understand the big picture. The Curriculum Principle of NCTM
recognizes that “mathematics is a highly interconnected and cumulative subject…therefore needs to
introduce ideas in such a way that they build on one another.” In addition, recent shifts in curriculum
paradigm support the idea of blended courses to teach related cross-curricular concepts together.
PearsonSchool.com
800-848-9500
Copyright© 2009 Pearson Education, Inc. or its affiliate(s). All rights reserved
MODULE
1: Fundamentals of Geometry
Lesson 1: Basic Geometric Figures
Essential Question: Why are some terms defined and some terms undefined?
Lesson 2: Finding Distance
Essential Question: What is the difference between equality and congruence?
Lesson 3: Finding Midpoints
Essential Question: Why does a segment have an infinite number of bisectors but only one midpoint?
Lesson 4: All About Angles
Essential Question: Why should adjacent angles never be named by their vertex only?
Lesson 5: Special Angle Pairs
Essential Question: Why are all angles that form a linear pair also supplementary, but not all angles that
are supplementary form a linear pair?
Lesson 6: Parallel Lines and Transversals
Essential Question: What relationships exist among the angles formed when two parallel lines are
intersected by a third line?
Lesson 7: Cumulative Review and Assessment
2: Reasoning and Proof
Lesson 1: Inductive Reasoning
Essential Question: What is the role of inductive reasoning in mathematics?
Lesson 2: Conditionals
Essential Question: How are definitions related to conditional statements?
Lesson 3: Deductive Reasoning
Essential Question: How is the structure of an argument related to the validity of its conclusion?
Lesson 4: Proofs in Algebra
Essential Question: How do proofs utilize deductive reasoning?
Lesson 5: Geometric Proofs
Essential Question: What are the characteristics of a two-column proof?
Lesson 6: Paragraph Proofs
Essential Question: How can you use an indirect proof in your everyday life?
Lesson 7: Cumulative Review and Assessment
3: Triangles
Lesson 1: Triangles
Essential Question: What does a triangle’s classification tell you about its sides and angles?
Lesson 2: Some Triangle Theorems
Essential Question: Can you find the measure of an angle in a triangle if you are given only one of the
other angles?
Lesson 3: Perimeter and Area of Triangles
Essential Question: How is the area of a triangle related to the area of a rectangle?
Lesson 4: Triangle Inequalities
Essential Question: How is it possible that some groups of three segments form a triangle and some do
not?
Lesson 5: Segments in Triangles
Essential Question: Which segments of a triangle can be either inside, on, and outside of a triangle?
Lesson 6: Coordinate Proof
Essential Question: How is a coordinate proof similar to and different from a two-column proof?
Lesson 7: Cumulative Review and Assessment
4: Congruent Triangles
Lesson 1: Congruent Triangles
Essential Question: How are the sides and angles of congruent triangles related?
Lesson 2: Tests for Congruent Triangles
Essential Question: What property exists in triangles that make them such a common shape in
construction?
Lesson 3: Proving Triangles Congruent
Essential Question: How can the Reflexive Property be used in proving two triangles congruent?
Lesson 4: Another Triangle Congruence
Essential Question: What advantages does a flow proof have over a two-column proof?
Lesson 5: Using Congruent Triangles
Essential Question: How can congruent triangles help you estimate the distance across a river?
Lesson 6: Proving Right Triangles Congruent
Essential Question: How does proving right triangles congruent compare to proving other types of
triangles congruent?
Lesson 7: Cumulative Review and Assessment
5: Properties of Quadrilaterals
Lesson 1: Properties of Quadrilaterals
Essential Question: What are the properties of a quadrilateral?
Lesson 2: Proving Quadrilaterals Are Parallelograms
Essential Question: How do you prove quadrilaterals are parallelograms?
Lesson 3: Classifying Quadrilaterals
Essential Question: How do you classify a quadrilateral?
Lesson 4: Perimeter and Area of Quadrilaterals
Essential Question: How do you use formulas to find perimeter and area of quadrilateral?
Lesson 5: Properties of Trapezoids and Kites
Essential Question: What are the properties of a trapezoid and a kite?
Lesson 6: Proofs
Essential Question: How can you prove a geometric statement with deductive reasoning?
Lesson 7: Cumulative Review and Assessment
6: Polygons
Lesson 1: Polygons
Essential Question: How are polygons classified?
Lesson 2: Angle Measures of Polygons
Essential Question: How are the interior and exterior angles of polygons determined?
Lesson 3: Perimeter and Area of Polygons
Essential Question: How do you find the perimeter and area of regular polygons?
Lesson 4: Changes in Dimensions and Their Effect in Perimeter and Area
Essential Question: How does changing the lengths of side affect the perimeter and the area of polygons?
Lesson 5: Composite Polygons
Essential Question: How do you find the perimeter and area of polygons?
Lesson 6: Tessellations
Essential Question: What types of polygons create tessellations?
Lesson 7: Cumulative Review and Assessment
7: Similarity
Lesson 1: Ratios and Proportions
Essential Question: How do you use ratios and proportions to solve problems?
Lesson 2: Using Proportions to Solve Geometric Problems
Essential Question: How do you calculate actual size from a scale drawing?
Lesson 3: Similar Polygons
Essential Question: How can you find missing measurements if two polygons are similar?
Lesson 4: Proving Triangles Similar Using AA, SSS, and SAS
Essential Question: In what ways are triangles similar?
Lesson 5: Proving Triangles Similar Using Geometric Proofs
Essential Question: How can you prove that triangles are similar?
Lesson 6: Proportionality Theorems and Geometric Mean
Essential Question: Are all parts of similar triangles similar?
Lesson 7: Cumulative Review and Assessment
8: Right Triangles
Lesson 1: Pythagorean Theorem
Essential Question: If you know the lengths of two sides of a right triangle, how do you find the third side?
Lesson 2: Pythagorean Theorem Applications
Essential Question: Given three side lengths of a triangle, how can you determine whether the triangle is
right, acute, or obtuse?
Lesson 3: Pythagorean Triples
Essential Question: How can you identify the remaining side of a right triangle quickly if you are given the
first two?
Lesson 4: Special Right Triangles
Essential Question: How do you find the lengths of the sides of a 30°-60°-90° triangle and a 45°-45°-90°
triangle?
Lesson 5: Trigonometric Ratios
Essential Question: How can I find the lengths of the triangle if it isn’t a special right triangle?
Lesson 6: Angles of Elevation and Depression
Essential Question: How can I find the lengths of a right triangle given the angle of elevation or
depression?
Lesson 7: Cumulative Review and Assessment
9: Circles
Lesson 1: Exploring Circles
Essential Question: How do you find the measure of an arc of a circle?
Lesson 2: Arcs and Chords
Essential Question: How can you tell if two chords in a circle are congruent?
Lesson 3: Tangents and Secants
Essential Question: How do you find the angle formed by two chords intersecting inside or outside a
circle?
Lesson 4: Tangent and Secant Segments
Essential Question: What are some properties of segments and arc lengths to a circle?
Lesson 5: Circumscribed and Inscribed Circles
Essential Question: What is the relationship between an inscribed angle and its intercepted arc?
Lesson 6: Equations of Circles
Essential Question: How do you find the equation of a circle?
Lesson 7: Cumulative Review and Assessment
10: Coordinate Geometry
Lesson 1: Distance and Midpoint Formulas
Essential Question: How do you use the distance and midpoint formulas to solve problems?
Lesson 2: Exploring Slope and Intercepts
Essential Question: How do you determine slope and the x- and y-intercepts from graphs and equations?
Lesson 3: Writing Equations of Lines
Essential Question: How do you write the equation of a line?
Lesson 4: Investigating Geometric Relationships of Lines
Essential Question: How do you use parallel and perpendicular lines in geometry?
Lesson 5: Properties of Vectors
Essential Question: How do you use vectors?
Lesson 6: Prove It!
Essential Question: How can you use the midpoint, distance, and slope formulas to prove geometric
figures?
Lesson 7: Cumulative Review and Assessment
11: Transformations
Lesson 1: Transformations and Reflections
Essential Question: How do you reflect or flip a figure?
Lesson 2: Translations
Essential Question: How do you translate or slide a figure?
Lesson 3: Rotations
Essential Question: How do you rotate or turn a figure?
Lesson 4: Glide Reflections
Essential Question: How do you combine movements like a slide and a reflection to get one result?
Lesson 5: Dilations
Essential Question: How do you change the size of a figure, but not its shape?
Lesson 6: Composite Transformations
Essential Question: How do you combine multiple transformations and get a finished movement?
Lesson 7: Cumulative Review and Assessment
12: Solid Geometry
Lesson 1: Prisms
Essential Question: When is a prism a oblique?
Lesson 2: Pyramids
Essential Question: What makes a pyramid regular?
Lesson 3: Cylinders
Essential Question: Why isn’t a cylinder a prism?
Lesson 4: Cones and Spheres
Essential Question: How do you find the area of a sphere?
Lesson 5: Similar Solids
Essential Question: How do you know if two solids are similar?
Lesson 6: Euler’s Theorem and Real World Problems
Essential Question: How does Euler’s formula work?
Lesson 7: Cumulative Review and Assessment