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Course Outline

 Teaching Units Competencies and Objectives Fundamental concepts Name and identify points, lines, planes, segments, rays, and angles. Determine midpoint and distance for points on a number line and on the Cartesian Plane. Measure and classify angles. Identify and use special angle pairs. Lines Write the equation of a line given its graph, its slope and a point, two points, or a table of values. Determine if lines are parallel, perpendicular, or neither using slope. Write the equation of a line that is parallel or perpendicular to a given line through a given point. Logic Make conjectures based upon inductive reasoning. Provide counterexamples. Create and interpret truth tables. Create and interpret Venn Diagrams. Identify the hypothesis and conclusion of a conditional statement. Create and determine the validity of the converse, inverse, and contrapositie of conditional statements. Create and determine the validity of biconditional statements. Use the Law of Detachment and Law of Syllogism to determine the validity of statements. Introduction to proofs Learn and use the Euclidean postulates. Construct algebraic proofs. Construct proofs about segments using the midpoint theorem and the segment addition postulate. Construct proofs about angles using the definition of anlge bisector and the angle addition postulate. Construct proofs about complementary and supplementary angles. Construct proofs involving right angles. Proving lines are parallel or perpendicular Identify corresponding, alternate interior, alternate exterior, and consecutive interior angles. Prove angles are congruent when parallel lines are cut by a transversal. Prove lines are parallel using angle properties. Use properties of parallel lines cut by a transversal and algebra to find angle measures. Congruent and similar polygons Solve proportions. Determine if two polygons are similar or congruent. Prove triangles are congruent or similar. Determine situations that create similar polygons. Use proportions to find missing lengths of polygons. Use proportional reasoning to determine perimeter and area of similar figures. Use properties of isosceles and equilateral triangles to find angle measures and side lengths. Use proportions to find angle measures when a line intersects a triangle that is parallel to one of its sides. Use properties of altitudes, angle bisectors, and medians of triangles to find angle measures and side lengths. Properties of right triangles Calculate the geometric mean. Use the geometric mean to determine missing lengths in right triangles with an altitude drawn from the right angle. Use the Pythagorean Theorem and its converse to find side lengths of right triangles, or determine if a triangle is a right triangle. Use properties of 30-60-90 and 45-45-90 triangles to find angle measures and side lengths. Write ratios for lengths of sides of right triangles using sine, cosine, and tangent. Use the inverse trigonometric functions to find angle measures. Use sine, cosine, and tangent to find missing side lengths in right triangles. Use sine, cosine, and tangent to solve problems involving angles of elevation and depression.

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