• Courses numbered 1 - 49 are remedial or college preparatory courses which do not apply toward an A. A. Degree and are not intended for transfer.
• Courses numbered 50-99 apply toward an AA Degree, but are not intended for transfer.
• Courses numbered 100 and higher apply toward an AA Degree and/or are intended for transfer to a four-year college or university.

Unit Value: 4  

Lecture Hours Per Week: 4  

Lab Hours Per Week:  

Lecture/Lab Hours Per Week:  

 

Requisite(s)
To satisfy a prerequisite, the student must have earned a letter grade of A, B, C or P(Pass) in the prerequisite course, unless otherwise stated.

Prerequisite:
A minimum grade of 'C' in MATH 50 or A minimum grade of 'C' in MATH 50B or eligibility determined through the math placement process

Corequisite:
None

Prerequisite: Completion of, or concurrent enrollment in
None

Recommended Preparation:
None

Limitation on Enrollment:
None

1. form conjectures using inductive reasoning;
2. distinguish between known facts and conjectures that should be proved;
3. prove results using definitions, postulates, and theorems, by deductive reasoning;
4. apply the basic definitions, postulates and theorems of geometry in solving problems;
5. develop critical thinking skills by solving high level, multi-step problems.

1. Lecture

1. Elements of Geometry.
   1. Meaning of sets.
      1. Representing sets, relationships between sets, Venn diagrams, real numbers, the number line, distance between points, absolute value.
   2. Points, lines, and planes.
      1. Basic undefined terms, essential definitions.
   3. Angles and their measurement.
      1. Angles, measurement of angles, some special angles and angle relationships.
   4. Additional definitions.
      1. Triangles, general polygons, quadrilaterals, circles, circles in relation to other figures, spheres.
2. Deduction and Proof.
   1. The meaning of deductive thinking.
      1. Inductive reasoning, deductive reasoning, if-then statements.
   2. Bases for proof.
      1. Deductive thinking in Algebra; definitions and postulates in geometry; properties of real numbers, equality and inequality.
   3. Initial postulates and theorems.
      1. Points, lines, and planes; lines and segments; deductive proofs.
3. Angle relationships; perpendicular lines.
   1. Angle relationships.
      1. Initial postulates and theorems; straight angles, right angles, and perpendicular lines.
   2. Formal proofs.
      1. Supplementary angels, complementary angles, vertical angles, the demonstration of a theorem.
4. Parallel lines and planes.
   1. When lines and planes are parallel.
      1. Basic properties, transversals and special angles, indirect proof.
   2. How to show that lines are parallel.
      1. The parallel postulate, converses of earlier statements about parallels, applying parallels to triangles.
5. Congruent triangles.
   1. Proving that triangles are congruent.
      1. Corresponding parts of two triangles, formal treatment of congruent triangles, more ways to prove triangles congruent, overlapping triangles.
   2. Using congruent triangles to prove segments and angles equal.
      1. Proving corresponding parts equal, isosceles triangles, applying properties of congruent triangles to quadrilaterals.
6. Similar polygons.
1. Some principles of Algebra.
   1. Ratio and proportion, special properties of a proportion.
2. What similarity means.
   1.  Similar polygons, similar triangles, properties of special segments in a triangle.
3. Similarity in right triangles.
   1. Properties of the altitude drawn to the hypotenuse in a right triangle, the Pythagorean theorem, special right triangles: 30-60-90 and 45-45-90.
4. Applying the Pythagorean theorem.
   1.  Right triangles in three-dimensional figures, projections into a plane.
5.  Right triangle trigonometry.
7. Circular arcs and angles.
   1. Measures of arcs and angles.
      1. Arcs and central angles, inscribed angles, other angles formed by secants and tangents.
   2. Lines and segments related to circles.
      1. Chords of the same circle or equal circles, proportions involving chords, secants, and tangents.
8. Constructions and loci.
   1. Constructions.
      1. What construction means; permissible instruments and basic angle constructions, constructing parallel lines and perpendicular lines, constructions involving circles, constructing special segments.
   2. Locus.
      1. The meaning of locus, intersection of loci, construction by means of loci.
9. Coordinate geometry.
   1. Relating points and numbers.
      1. Graphs on one axis, plotting points in two dimensions, symmetry, graphs meeting given conditions.
   2. Finding and using distances.
      1. The distance formula, the circle, the midpoint formula.
   3. The graphing of lines.
      1. The slope of a line, parallel, and perpendicular lines, writing equations of lines, additional properties of lines.
10. Areas of polygons and circles.
    1. Quadrilaterals and triangles.
       1. What area means: Basic postulates, and definitions, areas of rectangles and parallelograms, areas of triangles, and trapezoids, proofs involving areas, comparing areas of similar triangles.
    2. Areas of regular polygons.
       1. Special properties of a regular polygon, areas of regular polygons, comparing areas of similar polygons.
    3. Circles, sectors, and segments.
       1. The circle as limiting case of a regular polygon; area of a circle; arcs, sectors, and segments.
    4. Area constructions.
       1. Constructions involving a fourth proportional, constructions involving a square root.
11. Areas and volumes of solids.
    1. Prisms and Pyramids.
    2. Cylinders, cones and spheres.
    3. Areas and volumes of similar solids.

1. Lial, Margaret L., Arnold R. Stephensen, and L. Murphy Johnson. Essentials of Geometry for College Students. U.S.A.: HarperCollins, 1990.

• Exams/Tests
• Homework