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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 • • • • Chapter 1 Sections 1.1 – 1.6 Chapter 2 Chapter 3 • • • • • • • • • • • • • Congruence and Transformations 20 Days Chapter 4 All • • • • • Chapter 9 only 9.6 • • Similarity and Trigonometry 30 Days • Chapter 6 • • 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) • • • • • • • 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 • • • • • • • • Chapter 8 • Chapter 10 • • • • • 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 • • • • • • • • • 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.