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RCS Geometry Honors Pacing Guide SCS Objectives Essential Questions Key Concepts # Days 1.02 Use length, area, and volume of geometric figures to solve problems. 2.01 Use logic and deductive reasoning to draw conclusion and solve problems. 2.02 Apply properties, definitions, and theorems of angles and lines to solve problems and write proofs 2.03 Apply properties, definitions, and theorems of two-dimensional figures to solve problems and write proofs. What is inductive reasoning and how can you use it to find solutions? How can you find basic geometry terms within different figures? How do you use the distance formula to measure points, lines, etc.? What are different angles and their parts? How can you bisect and angle/segment? What is the perimeter and area of common figures? Patterns Inductive reasoning Point, lines, & planes Segments Angles Segment & angle bisectors Angle pair relationships Perimeter Circumference Area 4 2.01 Use logic and deductive reasoning to draw conclusion and solve problems. 2.02 Apply properties, definitions, and theorems of angles and lines to solve problems and write proofs. How can you use postulates about points, lines, and planes to analyze real-life objects? How do you rewrite postulates in a form suitable for problems solving? How do you determine whether a logic statement is valid? How can you use algebra to solve geometric equations? How can you prove statements about segments in real-life situations? How can you use properties of angle congruence to prove properties about pairs of angles? Conditional statements Biconditional statements Deductive reasoning Reasoning w/ algebra properties Proving segment statements Proving angle statements 4 2.01 Use logic and deductive reasoning to draw conclusion and solve problems. 2.02 Apply properties, definitions, and theorems of angles and lines to solve problems and write proofs. How do you describe lines and planes in real-life objects? Can you write and use different type of proofs and show how this is done? How can you prove and use results about parallel lines and transversals to understand the world around you? How do you know when lines are parallel? Can you use (and demonstrate the use of) properties of parallel lines? How can you write an equation of a line parallel to a given line in a coordinate plane? Lines Angles Perpendicular lines proof Parallel lines Transversals Proving lines are parallel Properties of parallel lines Parallel lines in a coordinate plane Perpendicular lines in a coordinate plane 5 RCS Geometry Honors Pacing Guide How do you use slope to decide whether lines are perpendicular? Can you find the distance from a point to a line? 2.01 Use logic and deductive reasoning to draw conclusion and solve problems. 2.02 Apply properties, definitions, and theorems of angles and lines to solve problems and write proofs. 2.03 Apply properties, definitions, and theorems of two-dimensional figures to solve problems and write proofs. How can you classify triangles by their sides and angles? How do you identify congruent figures and corresponding parts? How do you prove triangles are congruent using AAS theorem, SSS, SAS, and ASA postulates? How do you use congruent triangles to plan and write proofs? When are the properties of isosceles, equilateral, and right triangles applied? How can you prove triangles are congruent using coordinate geometry? Triangles Angles of triangles Congruence in triangles SSS SAS ASA AAS Using congruent triangles Isosceles Equilateral Right triangles Triangles & coordinate proof 5 1.02 Use length, area, and volume of geometric figures to solve problems. 2.02 Apply properties, definitions, and theorems of angles and lines to solve problems and write proofs. 2.03 Apply properties, definitions, and theorems of two-dimensional figures to solve problems and write proofs. How can you use perpendicular and angle bisectors to decide where a hockey goalie should be placed? How can you find the perpendicular and angle bisector of a triangle? Where can you use properties of medians and altitudes? How do you use properties of midsegments of a triangle? Why would you compare the length of the side or the measures of angles of a triangle? How can you show that you understand indirect proofs? Perpendiculars & bisectors Bisectors of a triangle Medians of a triangle Altitudes of a triangle Midsegment theorem Inequalities of one triangle Indirect proof-inequalities 2 triangles 7 1.02 Use length, area, and volume of geometric figures to solve problems. 2.02 Apply properties, definitions, and theorems of angles and lines to solve problems and write proofs. 2.03 Apply properties, definitions, and theorems of two-dimensional How do you identify different polygons? Can you find an unknown measure of an angle of a quadrilateral? How do you use the properties of a parallelogram? How can you use coordinate geometry with parallelograms? What are some properties of rectangles, squares, and rhombuses and how can you use them to simplify real-life Polygons (angle measures) Properties of parallelograms Proofs • Quadrilaterals • Parallelograms Rhombus Rectangles 8 RCS Geometry Honors Pacing Guide figures to solve problems and write proofs. tasks? What are the properties of trapezoids and kites? How can you prove that a quadrilateral is a special type of quadrilateral? What are the areas of rectangles, kites, parallelograms, squares, triangles, trapezoids, and rhombuses? Squares Trapezoids & kites Special quadrilaterals Areas of triangles Areas of quadrilaterals 1.02 Use length, area, and volume of geometric figures to solve problems. 2.03 Apply properties, definitions, and theorems of two-dimensional figures to solve problems and write proofs. 3.02 Use matrix operations (addition, subtraction, multiplication, and scalar multiplication) to describe the transformation of polygons in a coordinate plane. What is the ration of two numbers? Can you understand properties and proportions? How do you identify similar polygons and use properties of similar polygons? How would you prove tow triangles are similar using definitions and AA similarity postulate? Ratio Proportions Problem solving w/ proportions Similar polygons Similar triangles 4 1.01 Use the trigonometric rations to model and solve problems involving right triangles. 1.02 Use length, area, and volume of geometric figures to solve problems. 2.02 Apply properties, definitions, and theorems of angles and lines to solve problems and write proofs 2.03 Apply properties, definitions, and theorems of two-dimensional figures to solve problems and write proofs. How can you solve problems involving similar right triangles formed by the altitude drawn to the hypotenuse of a right triangle? What is the Pythagorean theorem? How do you use side lengths to classify triangles by their angle measure? When can you find side lengths of special triangles? How do you find trigonometric rations of an acute angle? How do you find the magnitude, direction, and sum of a vector? Similar right triangles Pythagorean theorem Converse of Pythagorean theorem Special Right triangles Trigonometric Ratios Solving Right Triangles Vectors 8 1.02 Use length, area, and volume of geometric figures to solve problems. 2.02 Apply properties, definitions, How can you identify and use properties of tangents of circles? How can you use properties of arcs and chords of circles to Circles Tangents to circles Arcs 7 RCS Geometry Honors Pacing Guide and theorems of angles and lines to solve problems and write proofs 2.03 Apply properties, definitions, and theorems of two-dimensional figures to solve problems and write proofs. solve problems? How can you use properties of inscribed angles and inscribed polygons of circles to reach conclusions about angles? How can you use angles formed by tangents, chords, and secants? How do you find the length of segments of tangents, chords, and lines that intersect a circle? How do you find and graph the equations of a circle? How do you draw loci in a plane that satisfy one or more conditions? Chords Inscribed angles Angle relationships Segment lengths in circles Equations of circles loci 1.02 Use length, area, and volume of geometric figures to solve problems. 2.02 Apply properties, definitions, and theorems of angles and lines to solve problems and write proofs 2.03 Apply properties, definitions, and theorems of two-dimensional figures to solve problems and write proofs. How can you find the measure of interior and exterior angles of a polygon? How do you find the areas of equilateral triangles and other polygons? How would you compare perimeters and areas of similar figures? How can you find the circumference of a circle and the length of an arc of a circle? What is geometric probability? Area of regular polygons Perimeters of similar figures Area of similar figures Circumference & Arc length Areas of Circles & sectors Geometric probability 7 1.02 Use length, area, and volume of geometric figures to solve problems. 2.03 Apply properties, definitions, and theorems of two-dimensional figures to solve problems and write proofs. 2.04 Develop and apply properties of solids to solve problems. How can you use properties of polyhedra to solve problems? How do you find the surface area of prisms and cylinders? How do you find the volume of prisms and cylinders? How do you find the surface area of pyramids and cones? How do you find the volume of pyramids and cones? How do you find the surface area and volume of a sphere? How do you find the surface area and volume of similar solids? Exploring solids Surface area & Volume • Prisms • Cylinders Surface Area & Volume • Pyramids • Cones Surface Area & Volume • Spheres Similar Solids 7 2.02 Apply properties, definitions, and theorems of angles and lines to How can you identify type of rigid transformations? How can you use properties of reflection? Rigid Motion in a plane Reflections 7 RCS Geometry Honors Pacing Guide solve problems and write proofs. 3.01 Describe the transformation (translation, reflection, rotation, dilation) of polygons in the coordinate plane in simple algebraic terms. 3.02 Use matrix operations (addition, subtraction, multiplication, and scalar multiplication) to describe the transformation of polygons in a coordinate plane. How do you relate rotations and rotational symmetry? How do you use properties of translation? How do you use properties of glide reflection? How do you classify frieze patterns? Rotations Translation & vectors Glide reflections Compositions Frieze Patterns