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CHICAGO HIGH SCHOOL FOR AGRICULTURAL SCIENCES GEOMETRY COURSE OUTLINE 2009-2010 Semester One POINTS, LINES, PLANES, AND ANGLES Identify and model points, lines, and planes. 9B1a Identify collinear and coplanar points and intersecting lines and planes in space. 9B1a Measure segments and determine accuracy of measurement and compute with measures. 6C5, 7B3 Find the distance between two points. 7A4b, 9C3b Find the midpoint of a segment. 9C3b Measure and classify angles. 7A3b, 9B1b Identify and use congruent angles and the bisector of an angle. 9B1a Identify and use special pairs of angles. 9B1a Identify perpendicular lines. 9B1a Identify and name polygons and find their perimeters. 7A4b, 9B1a As result of the above, the student will be able to have the basic building blocks used in geometry and use these blocks to describe real-world objects. REASONING AND PROOF Make conjectures, determine whether a statement is true or false, and find counterexamples for statements. 9C4a & b Use deductive reasoning to reach valid conclusions. 9C4a & b Verify algebraic and geometric conjectures using informal and formal proof. 9C4c, 8A3c Write proofs involving segment and angle theorems. 9C4c As result of the above, the student will be able to solve problems and reach conclusions using logic and reasoning. PARALLEL AND PERPENDICULAR LINES Identify angle relationships that occur with parallel lines and a transversal.9B2 Identify and prove lines parallel from given angle relationships.9B2 Use slope to analyze a line and to write its equation. 8B4a Find the distance between a point and a line and between two parallel lines.9C3b As result of the above, the student will be able to identify special angle relationships, review slope and forms for the equation of a line, solve problems by writing linear equations, use slope to determine whether lines are parallel, perpendicular or neither and find the distance between a point and a line. CONGRUENT TRIANGLES Classify triangles. 9B4 Apply the Angle Sum Theorem and the Exterior Angle Theorem.9B1b Identify corresponding parts of congruent triangles. 9C4b Test for triangle congruence using SSS, SAS, ASA, and AAS. 9B4 Use properties of isosceles and equilateral triangles. 9C4c Write proofs. As result of the above, the student will be able to learn about the properties of congruent triangles & properties of isosceles and equilateral triangles, apply the angle sum and exterior angle theorems and prove triangles are congruent using SSS, SAS, ASA and AAS. RELATIONSHIPS IN TRIANGLES Identify and use perpendicular bisectors, angle bisectors, medians and altitudes in triangles. 9B2 Apply properties of inequalities relating to the measures of angles and sides of triangles. 9B2 Apply the Triangle Inequality Theorem. 9B2 As result of the above, the student will be able to expand their knowledge of triangles and their properties, identify bisectors, medians, and altitudes and apply properties of inequalities related to the measure of angles and sides and the theorem of Triangle Inequality. PROPORTIONS AND SIMILARITY 6D4 Review the terms, ratio and proportions, and how to solve equations with proportions. 6D3 & 4 Identify similar figures and similar triangles. 6D4, 9A3c Solve problems involving scale factors. 6D4, 9A3c Use similar triangles to solve problems. 6D4, 8D3b, 9B4 Use proportional parts of triangles. 6D4, 9A3c As result of the above, the student will be able to develop and solve proportions using similar figures or triangles. 1 Semester Two RIGHT TRIANGLES AND TRIGONOMETRY Find the geometric mean between two numbers. 7A4b, 10A4a Solve problems involving relationships between parts of a right triangle and the altitude to its hypotenuse. 9C3b Use the Pythagorean theorem and its converse. 9D3 Identify Pythagorean Triples. 9D3 Use the properties of 45-45-90 and 30-60-90 triangles. 9C3b Find trigonometric ratios using right triangles and solve problems using trigonometric ratios. 9D4 As result of the above, the student will be able to find the geometric mean between two numbers and work with right triangles to find the measure of missing sides or angles using the geometric mean, the Pythagorean Theorem, the properties of the special right triangles and/or Trigonometry. QUADRILATERALS Find the sum of the interior angles and the sum of the exterior angles of a polygon. 7A3b Recognize and apply properties of the sides, angles and diagonals of parallelograms, rectangles, squares, rhombi and trapezoids. 9B4 Solve problems involving the medians of trapezoids. 9B4 As result of the above, the student will be able to solve problems involving the interior angles and exterior angles of polygons and will be able to determine what type of quadrilateral is given by using properties given. CIRCLES Identify parts of a circle and solve problems involving circumference. 9B4 Find arc and angle measures in a circle. 7A4b Find measures of segments in a circle. 7A4b Write an equation of a circle. 8B2 As result of the above, the student will be able to identify and solve problems involving circles. AREAS OF POLYGONS AND CIRCLES Find areas of rectangles, squares, parallelograms, triangles, rhombi, trapezoids, regular polygons, and circles. 7A4b Find areas of irregular figures. 7B5b Find geometric probability and areas of sectors and segments of circles. 7A4b, 10C4a As result of the above, the student will be able to find the areas of: polygons, circles, circle sectors and irregular figures and will determine the geometric probability. SURFACE AREA Identify three-dimensional figures and their parts. 9A4a Find the lateral area and surface area of prisms, cylinders, pyramids, and cones. 7A4b Find the surface area of spheres and hemispheres. As result of the above, the student will be able to identify and find the surface areas of three-dimensional figures. 7A4b VOLUME Find the volumes of prisms, cylinders, pyramids, cones, and spheres. 7A4b, 7B5 Graph solids in space. 9C5b Use the Distance and Midpoint Formulas for points in space. 7A4b As result of the above, the student will be able to find the volume of three-dimensional figures and find the distance or midpoints of points in space. TRANSFORMATIONS Name, draw, and recognize figures that have been reflected, translated, or rotated. 7B5, 10A4a, 10B4 Textbooks: Glencoe Mathematics Geometry - Illinois Edition 2005 2