Honors Geometry A Grades: 9, 10, 11, 12 Credits: 0.50 Prerequisites: Successful completion of Algebra 1 Description: This course is the first of two that comprise Honors Geometry. In this course, the student will explore geometry concepts and apply them to real-world problems. The student will begin by defining basic geometric terms, postulates, and theorems before learning how to apply them to parallel and perpendicular lines. Next, the student will explore relationships in triangles, quadrilaterals, and other polygons. Throughout the course, the student will be introduced to many higher mathematical concepts and applications. Units: Tools of Geometry This unit introduces various topics in geometry. The beginning of the unit involves representing threedimensional solid figures using nets, isometric drawings, and orthographic drawings. Special drawing techniques are introduced, such as slanted lines to represent three-dimensional perspective and dashed lines to represent hidden lines. An introduction to basic geometry terms such as points, lines, and planes is included. These are introduced as the building blocks of geometry on which all other geometry terms are defined. Postulates and axioms are introduced as well as naming techniques.measuring segments and angles are introduced along with the Ruler Postulate, Segment Addition Postulate, Protractor Postulate, and Angle Addition Postulate. Types of angles as well as special angle pairs and their relationships are included. The degree unit is introduced and the use of a protractor to find angle measure is included. A ruler is also used to find segment length. Problems involving algebra, such as solving linear equations, are used to find segment lengths and angle measures. The concept of creating constructions without the use of measurement by using only a straightedge and protractor is introduced in this unit. Four basic constructions are included, such as constructing congruent segments, congruent angles, perpendicular bisectors, and angle bisectors. These constructions will be used to create other constructions, such as an equilateral triangle. They will also be used to solve problems, such as creating a 45 o angle.
The unit concludes with finding the midpoint of segments on a number line and on a coordinate plane using the midpoint formulas. The distance formula is used to find the distance between two points in a coordinate place. Algebra skills are reviewed as necessary for solving problems using midpoint and distance formulas. Other formulas included at the end of the unit are formulas used to find perimeter, circumference, and area of geometric figures such as squares, rectangles, triangles, and circles. The area of a region is also explored. Many new vocabulary terms associated with the topics are included. A variety of real-world applications are embedded throughout the unit. A variety of activities are also used to enhance instruction, such as BrainPOP movies, Gizmos, Discovery Education streaming movies, SkillsTutor, and PowerGeometry. Assessments in Unit 1 include quick checks, quizzes, a unit portfolio involving origami, a discussion on how math is used in daily life, and a Unit Test. Standard Geometry This unit focuses on topics related to reasoning and writing formal proofs. In the beginning of this unit, students will observe patterns in numeric and geometrical sequences and use inductive reasoning to make conjectures. Then conditional statements are explored, including converses, inverses, and contrapositives. Biconditionals are used to help define and create good definitions. Formal notation is emphasized in the use of a truth table to examine the validity of an argument. The unit continues with students exploring deductive reasoning using both the Law of Detachment and Law of Syllogism. These reasoning skills will be applied to evaluate a set of clues and then formulate a possible solution. Students will then use deductive reasoning and the Properties of Equality to justify steps when solving an equation. The conclusion of the unit introduces two types of formal proofs, two-column proofs and paragraph proofs. Properties of Congruence as well as theorems involving angles are included. Students will learn how to set-up a two-column proof and will be given tips on writing formal proofs. Acceptable reasons to use in proofs are specified. Students will be assessed through-out the unit with a variety of assessments, such as quick checks, quizzes, a portfolio project involving how Greeks used deductive reasoning and mathematics, a discussion on inductive and deductive reasoning, and a unit test. Parallel and Perpendicular Lines In this unit, you will explore concepts associated with parallel and perpendicular lines. You will begin by identifying parallel, perpendicular, and skew lines, as well as parallel and perpendicular planes. You will prove the theorems and postulate for the special angle pairs and use them to find angle measures. Then
you will use the converse of these theorems and postulate to prove lines parallel. You will also learn the different forms of proofs, such as two-column, paragraph, and flow proofs. You will practice using different theorems and making new constructions. Finally, you will apply concepts related to linear equations in a coordinate plane, and slope relationships of parallel and perpendicular lines. Congruent Triangles This unit covers concepts associated with congruent triangles, such as identifying corresponding parts of congruent triangles, identifying isosceles and equilateral triangles, proving triangles congruent, and proving parts of triangles congruent. Lessons build on students' understanding and skills related to angles and triangles. Visualization skills are used for overlapping triangles. Theorems and postulates such as SSS, SAS, ASA, AAS, and HL are introduced throughout the unit. The definition corresponding parts of congruent triangles are congruent (CPCTC) is used to prove parts of triangles congruent. Students will use and apply properties of isosceles and equilateral triangles. Students will also prove two triangles congruent using other congruent triangles. The difference between congruence and similarity is introduced for further units of study. A variety of methods are used throughout the unit for instruction, practice, and review of concepts. Students will complete worksheets and online practice for various concepts. Math writing journal activities require students to relate concepts to real-world applications and apply their knowledge in order to respond to thought-provoking questions. Hands-on exploration activities are provided through the Concept Byte activities in the textbook. Online and interactive activities, such as Teachlet tutorials, SkillsTutor, and Gizmos are used to further students' understanding of concepts. Various assessments are used throughout the unit to measure student progress such as Quick Checks, quizzes, and a unit test. Students will also complete a unit portfolio which involves viewing a Discovery Education streaming movie about the role of math in the design, technology, and construction of modern skyscrapers and ancient Greek architecture using triangles. Students will then complete related tasks involving architecture and triangles to complete the portfolio. Triangles In this unit, students will be discovering, exploring, and learning concepts involving relationships within triangles. Students will expand on the skills learned in previous units, such as using the midpoint formula to find the midsegments of triangles and the distance formula to examine relationships in triangles. New theorems are introduced, such as the Triangle Midsegment Theorem, Perpendicular Bisector Theorem, Angle Bisector Theorem, and Hinge Theorem. Also included are theorems related to concurrency in triangles and triangle inequality. There will be an emphasis on coordinate geometry and applications to linear equations. Students will explore relationships within a triangle using the Comparison Property of Inequality and the Corollary to the Triangle Exterior Angle Theorem, as well as those theorems related
to triangle inequality. The relationships between two triangles will be explored through the Hinge Theorem and its converse. Students will identify and use properties of midsegments, perpendicular bisectors, angle bisectors, medians, altitudes, and inequalities involving angles and sides of triangles through a variety of activities. These activities are designed and used for instruction, review, and practice of concepts in order to engage students throughout the Unit. Activities in this unit include Teachlet tutorials, worksheets, writing journal activities, Gizmos, and online interactive activities aligned to the textbook through PowerGeometry. A variety of assessments are used throughout the unit to gauge student comprehension of concepts. Self-check assessments are embedded in each lesson and provide students with feedback. A portfolio is used to assess concepts of inequalities in a triangle which requires students to complete three activities using straws of various lengths to create triangles. Other assessments include Quick Checks, quizzes, and a unit test. Polygons and Quadrilaterals In this unit, students will examine properties of quadrilaterals and use the properties to prove and classify special types of quadrilaterals, such as parallelograms, rectangles, rhombuses, squares, trapezoids, and kites. Properties of parallel and perpendicular lines and diagonals will be used to classify quadrilaterals. Students will use theorems to find angle measures of polygons, both interior and exterior angles. Geometry in the coordinate plane will be explored through classifying polygons in the coordinate plane using formulas such as slope, midpoint, and distance, as well as naming coordinates using variables for a general polygon and proving theorems using coordinate proofs. Students will be exposed to the polar graphing system. Various activities are used throughout the unit to support student learning. Students are encouraged to create and use Venn diagrams to show the relationships among polygons, equilateral polygons, equiangular polygons, and regular polygons. Interactive Gizmos are used throughout the unit to explore angle sums of polygons, properties of special parallelograms, and to classify quadrilaterals. Worksheets will help to review vocabulary, enhance instruction, and practice concepts. Students will view a BrainPOP movie clip on the types of triangles. Teachlet tutorials and homework video tutors are used throughout the unit to aid instruction. Online practice and math writing journal activities are used to encourage student thinking and understanding of various concepts. Self-check activities, feedback, and assessments are embedded throughout the unit. A portfolio on the coordinate grid system throughout history and a discussion on the coordinate proof serve as assessments. Other assessments include Quick Checks, quizzes, and a unit test.
Semester A Exam and Review This unit reviews concepts from Semester A of the Geometry course. The unit begins with a review assignment that helps students recall topics from Units 1 6. A matching and vocabulary activity explores special terms and properties from the course. Practice opportunities such as online practice, textbook problems, and worksheets are included. The assessment is included at the conclusion of the unit in the form of the semester exam. Course Sets Geometry (B, S, H, GT Math 8) Online Text/eBook itext Geometry: On Level Textbook/Novel Geometry: On Level