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1 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 realworld. There is a need to be able to visualize the movement and orientation of two and threedimensional 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 crosscurricular concepts together. PearsonSchool.com Copyright 2009 Pearson Education, Inc. or its affiliate(s). All rights reserved
2 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? 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 twocolumn proof? Lesson 6: Paragraph Proofs Essential Question: How can you use an indirect proof in your everyday life?
3 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 twocolumn proof? 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 twocolumn 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?
4 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? 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?
5 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? 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 triangle and a 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?
6 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? 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 yintercepts 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?
7 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? 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?
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