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1 Tools of Geometry This Chapter Begins by Addressing the Building Blocks of Geometry Which Are the Point, the Line, and the Plane Texas Geometry Textbook Table of Contents 1 Tools of Geometry This chapter begins by addressing the building blocks of geometry which are the point, the line, and the plane. Students will construct line segments, midpoints, bisectors, angles, angle bisectors, perpendicular lines, parallel lines, polygons, and points of concurrency. A translation is a rigid motion that preserves the size and shape of segments, angles, and polygons. Students use the coordinate plane and algebra to determine the characteristics of lines, segments, and points of concurrency. Standards: G.2A, G.2B, G.3A, G.3B, G.3C, G.4A, G.5B, G.5C, G.6D, G.9B Lesson Lesson Title Lesson Subtitle TEKS Key Math Objectives Key Terms • Point • Line • Collinear points • Plane • Compass • Identify and name points, lines,planes, rays, and line segments. • Straightedge • Use symbolic notation to describe points, lines, planes, rays, and • Sketch Points, Lines, Planes, Let's Get This line segments. • Draw Rays, and Line G.4A 1.1 • Describe possible intersections of lines and planes. • Construct Started! Segments • Identify construction tools. • Coplanar lines • Distinguish between a sketch, a drawing, and a construction. • Skew lines • Ray • Endpoint of a ray • Line segment • Endpoints of a line segment • Congruent line segments • Pythagorean triple • Distance Formula • Transformation G.2B • Apply Pythagorean triples to solve problems. • Rigid motion G.3A • Determine the distance between two points. • Translation Translating and G.3B • Use the Pythagorean Theorem to derive the Distance Formula. • Pre-image Constructing Line 1.2 Let's Move! G.3C • Apply the Distance Formula on the coordinate plane. • Image Segments G.5B • Translate a line segment on the coordinate plane. • Arc G.9B • Copy or duplicate a line segment by construction. CONSTRUCTIONS • Copying a lint segment • Duplicating a line segment • Determine the midpoint of a line segment on a coordinate plane. • Midpoint • Use the Midpoint Formula. • Midpoint Formula G.2A Midpoints and • Apply the Midpoint Formula on the coordinate plane. • Segment bisector G.2B 1.3 Treasure Hunt Bisectors • Bisect a line segment using patty paper. G.5B • Bisect a line segment by construction. CONSTRUCTIONS • Locate the midpoint of a line segment. • Bisecting a line segment 08/19 Texas Geometry Textbook: Table of Contents 1 Texas Geometry Textbook Table of Contents Lesson Lesson Title Lesson Subtitle TEKS Key Math Objectives Key Terms • Angle • Angle bisector G.3A Translating and • Translate an angle on the coordinate plane. G.3B Constructing Angles • Copy or duplicate an angle by construction. CONSTRUCTIONS 1.4 It's All About Angles G.3C and Angle Bisectors • Bisect an angle by construction. • Copying an angle G.5B • Duplicating an angle • Bisecting an angle • Derive the slope formula. • Determine whether lines are parallel. • Identify and write the equations of lines parallel to given lines. Parallel and Did You Find a G.2B • Determine whether lines are perpendicular. Perpendicular Lines on • Point-slope form 1.5 G.2C • Identify and write the equations of lines perpendicular to given Parking Space? the Coordinate Plane lines. • Identify and write the equations of horizontal and vertical lines. • Calculate the distance between a line and a point not on a line. • Construct a perpendicular line to a given line. • Construct a parallel line to a given line through a point not on the line. • Perpendicular bisector • Construct an equilateral triangle given the length of one side of the Constructing triangle. Making Copies— Just CONSTRUCTIONS Perpendicular Lines, G.5B • Construct an isosceles triangle given the length of one side of the • A perpendicular line to a given line 1.6 as Perfect as the Parallel Lines, and G.5C triangle. through a point on the line Original! Polygons • Construct a square given the perimeter (as the length of a given • A perpendicular line to a given line line segment). through a point not on the line • Construct a rectangle that is not a square given the perimeter (as the length of a given line segment). • Concurrent • Point of concurrency • Circumcenter G.5B • Construct the incenter, circumcenter, centroid, and orthocenter. • Incenter Points of Concurrency G.5C 1.7 What's the Point? • Locate points of concurrency using algebra. • Median G.6D • Centroid • Altitude • Orthocenter G.2B In the MATHia software, students identify and write names for geometric entities. They write measure statements G.2C for segments and angles. Students solve mathematical and real• world problems involving parallel and Learning Individually with MATHia or Skills Practice G.4A perpendicular lines on the coordinate plane. G.5A 08/19 Texas Geometry Textbook: Table of Contents 2 Texas Geometry Textbook Table of Contents 2 Introduction to Proof This chapter focuses on the foundations of proof. Paragraph, two-column, construction, and flow chart proofs are presented. Proofs involving angles and parallel lines are completed. Standards: G.4A, G.4B,G.4C, G.4D, G.5A, G.5B, G.6A Lesson Lesson Title Lesson Subtitle TEKS Key Math Objectives Key Terms • Induction • Deduction • Define inductive and deductive reasoning. • Counterexample • Identify methods of reasoning. • Conditional statement • Compare and contrast methods of reasoning. G.4B • Propositional form Foundations for Proof • Create examples using inductive and deductive reasoning. 2.1 A Little Dash of Logic G.4C • Propositional variables • Identify the hypothesis and conclusion of a conditional statement. • Hypothesis • Explore the truth values of conditional statements. • Conclusion • Use a truth table. • Truth value • Truth table • Supplementary angles • Complementary angles • Adjacent angles • Linear pairs • Calculate the complement and supplement of an angle. • Vertical angles And Now From a New Special Angles and G.4A • Classify adjacent angles, linear pairs, and vertical angles. • Postulate 2.2 Postulates G.4D • Differentiate between postulates and theorems. Angle • Theorem • Differentiate between *Euclidean and non-Euclidean geometries. • Euclidean geometry • Linear Pair Postulate • Segment Addition Postulate • Angle Addition Postulate • Additional Property of Equality • Subtraction Property of Equality • Reflexive Property • Substitution Property • Use the addition and subtraction properties of equality. • Transitive Property Paragraph Proof, • Use the reflexive, substitution, and transitive properties. G.4A • Flow chart proof Two-Column Proof, • Write a paragraph proof. G.5B • Two• column proof 2.3 Forms of Proof Construction Proof, • Complete a two-column proof. G.6A • Paragraph proof and Flow Chart Proof • Perform a construction proof. • Construction proof • Complete a flow chart proof. • Right Angle Congruence Theorem • Congruent Supplement Theorem • Congruent Complement Theorem • Vertical Angle Theorem 08/19 Texas Geometry Textbook: Table of Contents 3 Texas Geometry Textbook Table of Contents Lesson Lesson Title Lesson Subtitle TEKS Key Math Objectives Key Terms • Corresponding Angle Postulate • Use the Corresponding Angle Postulate. • Conjecture G.4A • Prove the Alternate Interior Angle Theorem. Angle Postulates and • Alternate Interior Angle Theorem G.5A • Prove the Alternate Exterior Angle Theorem. 2.4 What's Your Proof? Theorems • Alternate Exterior Angle Theorem G.6A • Prove the Same• Side Interior Angle Theorem. • Same• Side Interior Angle Theorem • Prove the Same• Side Exterior Angle Theorem. • Same• Side Exterior Angle Theorem • Converse • Corresponding Angle Converse Postulate • Alternate Interior Angle Converse G.4A Theorem G.4B Parallel Line Converse • Alternate Exterior Angle Converse G.5A • Write and prove parallel line converse conjectures. 2.5 A Reversed Condition Theorems Theorem G.5B • Same• Side Interior Angle Converse G.6A Theorem • Same• Side Exterior Angle Converse Theorem In the MATHia software, students calculate angle measures and justify their reasoning. They use flowchart proofs G.5A and two-column proofs to prove various line and angle theorems. They use theorems to solve mathematical prob- Learning Individually with MATHia or Skills Practice G.6A lems related to geometric figures. 08/19 Texas Geometry Textbook: Table of Contents 4 Texas Geometry Textbook Table of Contents 3 Perimeter and Area of Geometric Figures on the Coordinate Plane In this chapter, students investigate strategies for determining the perimeters and areas of rectangles, triangles, non-rectangular parallelograms, trapezoids, and composite plane figures on the coordinate plane. Students also explore the effects of proportional and non-proportional changes to the dimensions of a plane figure on its perimeter and area. Standards: G.2A, G.2B, G.3B, G.10B, G.11B Lesson Lesson Title Lesson Subtitle TEKS Key Math Objectives Key Terms • Determine the areas of squares on a coordinate plane. Transforming to a Using Transformations • Connect transformations of geometric figures with number sense 3.1 G.3B New Level! to Determine Area and operations. • Determine the areas of rectangles using transformations. • Determine the perimeter of triangles on the coordinate plane. • Determine the area of triangles on the coordinate plane. Looking at Area and Perimeter of • Determine and describe how proportional and non-proportional G.3B Triangles on the Coor- changes in the linear dimensions of a triangle affect its perimeter 3.2 Something Familiar G.10B in a New Way dinate Plane and area. • Explore the effects that doubling the area has on the properties of a triangle. • Determine the perimeter
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