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Geometry

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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