GREE CASTLE A TRIM HIGH SCHOOL PLA ED COURSE Board Approved: March 2010 COURSE TITLE: GEOMETRY GRADE LEVEL (S): 9, 10, 11 COURSE TEXT: GEOMETRY, HOLT/RINEHART/WINSTON, 1991 EDITION LIST OF TOPICS: REVIEW EQUATION SOLVING REVIEW LITERAL EQUATIONS REVIEW FACTORING LINES COMPLEMENTARY, SUPPLEMENTARY, AND VERTICAL ANGLES ANGLES AND PARALLEL LINES DISTANCE FORMULA ANGLES OF A TRIANGLE CLASSIFICATION OF TRIANGLES ISOSCELES TRIANGLES TRIANGLE INEQUALITY THEOREM PYTHAGOREAN THEOREM GEOMETRIC MEAN PERIMETER OF TRIANGLES AREA OF TRIANGLES TRIGONOMETRIC FUNCTIONS IN RIGHT TRIANGLES SOLVING RIGHT TRIANLGES USING TRIGONOMETRY SPECIAL RIGHT TRIANGLES (45-45-90 AND 30-60-90) LAW OF SINES AND COSINES CONGRUENT TRIANLGES SIMILAR TRIANGLES WITH PROPORTIONS CIRCUMFERENCE OF CIRCLES AREA OF CIRCLES WORD PROBLEMS AND APPLICATION OF CIRCUMFERENCE OF CIRCLE ROTATIONS
ARC LENGTH CENTRAL ANGLES AREA OF SECTORS AREA OF SHADED REGION IN CIRCLES SPECIAL RULES WITH CHORDS, SECANTS, AND TANGENTS OF CIRCLES PROPERTIES OF PARALLELOGRAMS PERIMETER AND AREA OF PARALLELOGRAMS RECTANGLES (PROPERTIES, PERIMETER, AREA) SQUARES (PROPERTIES, PERIMETER, AREA) RHOMBI (PROPERTIES, PERIMETER, AREA) TRAPEZIODS (PROPERTIES, PERIMETER, AREA) POLYGONS-CLASSIFICATIONS INTERIORS AND EXTERIOR ANGLES (SUM OF ANGLES, INDIVIDUAL ANGLE MEASUREMENT) AREA OF POLYGONS TWO-COLUMN PROOF RIGHT TRIANGLE CONGRUENCY AS TIME PERMITS: PSSA QUESTIONS, SAT AND COLLEGE ENTRANCE EXAM QUESTIONS VOLUME AND SURFACE AREA OF SPHERES VOLUME AND SURFACE AREA OF CYLINDERS VOLUME AND SURFACE AREA OF PRISMS VOLUME AND SURFACE AREA OF PYRAMIDS VOLUME AND SURFACE AREA OF CONES M 11.D.2.1 2.8.11 Review equation solving Last Revised February 15, 2008 Write, solve and/or graph linear equations and inequalities using various methods. Algebra and Functions 2.8.11 Review literal equations Algebra and Functions
M 11.D.2.2.2 2.8.11 Review factoring Factor algebraic expressions, including difference of squares and trinomials. Algebra and Functions M11.C.3.1.2 Slopes of lines (parallel and perpendicular) Relate slope to perpendicularity and/or parallelism. M11.C.1.2.1 Complementary, supplementary, and vertical angles Identify and/or use properties of triangles (e.g., medians, altitudes, angle bisectors, side/angle relationships M11.C.1.2 Angles and Parallel lines Recognize and/or apply properties of angles triangles. M11.C.3.1 Distance formula Solve problems using analytic geometry M11.C. 1.2 Angles of a triangle Recognize and/or apply properties of angles triangles
M11. C.1.2 Classification of triangles Recognize and/or apply properties of angles triangles M11. C.1.2 Isosceles triangles Recognize and/or apply properties of angles triangles M11.C.1.2.1 Triangle Inequality Theorem Identify and/or use properties of triangles (e.g., medians, altitudes, angle bisectors, side/angle relationships, Triangle Inequality Theorem) M11. C.1.4.1 Pythagorean Theorem Find the measure of a side of a right triangle using the Pythagorean Theorem. (Pythagorean Theorem included on the reference sheet.) M11.C.1.3.1 Geometric Mean Identify and/or use properties of congruent and similar polygons or solids.
M11. C.1.2 Perimeter of triangles Recognize and/or apply properties of angles, triangles, M11. C.1.2 Area of triangles Recognize and/or apply properties of angles, triangles, 2.10.11 B Trigonometric functions in right triangles 2.10.11 B Solving Right Triangles using Trigonometry 2.10.11 B Special right triangles (30-60-90 and 45-45-90) Identify, create and solve practical problems involving right triangles using the trigonometric functions and the Pythagorean theorem. Identify, create and solve practical problems involving right triangles using the trigonometric functions and the Pythagorean theorem. Identify, create and solve practical problems involving right triangles using the trigonometric functions and the Pythagorean theorem. 2.10.11 B Law of Sines and Cosines Identify, create and solve practical problems involving right triangles using the trigonometric functions and the Pythagorean theorem.
M11.C.1.3 Congruent Triangles Use Properties of congruence, correspondence and similarity in problem solving settings involving two- and three dimensional figures. M11.C.1.3.1 M11.C.1.3 M11.C1.1.1 M11.B.2.2 Similar Triangles with proportions Circumference of circles Use Properties of congruence, correspondence and similarity in problem solving settings involving two- and three dimensional figures. Identify and/or use properties of congruent and similar triangles. Identify and/or use the properties of a radius, diameter and/or tangent of a circle (given numbers should be whole) Use and/or develop procedures to determine or describe measures of perimeter, circumference, area, surface area and/or volume. M11.B.2.2 Area of circles Use and/or develop procedures to determine or describe measures of perimeter, circumference, area, surface area and/or volume. M11.B.2.2.3 M11.2.2 Word Problems and Applications of Circumference of a Circle Estimate area, perimeter or circumference of an irregular figure. Use and/or develop procedures to determine or describe measures of perimeter, circumference, area, surface
area and/or volume 2.9.11 H Rotations Construct a geometric figure and its image using various transformations M11.C1.1.2 Arc Length Identify and/or use properties of arcs, semicircles, inscribes angles and/or central angles. M11.C1.1.2 Central Angles Identify and/or use properties of arcs, semicircles, inscribes angles and/or central angles. M11.C1.1.2 Area of Sectors Identify and/or use properties of arcs, semicircles, inscribes angles and/or central angles.
M11.C.1.1.2 Area of shaded region in circles Identify and/or use properties of arcs, semicircles, inscribes angles and/or central angles. 2.9.11 F Special rules with chords, secants, and tangents of circles M11.C.1.2.2 Properties of Quadrilaterals including perimeter and area of Parallelogram, Rectangles, Squares, Rhombi, and Trapezoids 2.9.11 E Polygons- Classification and Area Use the properties of angles, arc, chords, tangents and secants to solve problems involving circles. Identify and/or use properties of quadrilaterals (e.g., parallel sides, diagonals, bisectors, congruent sides/angles and supplementary angles. Solve problems involving inscribed and circumscribed polygons. 2.9.11 E Interiors and Exterior angles (Sum of Angles, Individual Angle Measurement) Solve problems involving inscribed and circumscribed polygons. 2.9.11 Two-column Proof
M11.C.1.2 Right Triangle Congruency Recognize and/or apply properties of angles, triangles. M11.B.2.2.2 M11.B.2.2.1 Volume of Spheres, Cylinders, Prisms, Pyramids and Cones Surface Area of Spheres, Cylinders, Prisms, Pyramids and Cones Calculate the volume of prisms, cylinders, cones, pyramids and/or spheres. Formulas are provided on the reference sheet. Calculate the surface area of prisms, cylinders, cones, pyramids and/or spheres. Formulas are provided on the reference sheet.