Geometry –

mth432

(3 credits)

This course is designed to have students demonstrate the ability to use fundamental concepts of geometry including definitions, basic constructions, tools of geometry, and to recognize geometry as an axiomatic system.
This undergraduate-level course is weeks. This course is available as part of a degree or certificate program. To enroll, speak with an Enrollment Advisor.

Triangles

  • Construct triangles including altitude and the median parts.
  • Use congruent and right triangles to prove statements and theorems.
  • Construct a triangle congruent to a given triangle.
  • Use geometric theorems to prove how triangles are congruent.
  • Classify triangles by their sides and angles.

Solid Geometry

  • Calculate the surface area and volume of prisms, pyramids, cylinders, cones, and spheres.
  • Define solid figures that form in space.
  • Identify the behavior of lines and planes in space.

Similar Polygons and the Pythagorean Theorem

  • Demonstrate the applications of the Pythagorean Theorem.
  • Construct proportional segments of polygons.
  • Apply the postulates and theorems of similar polygons.
  • Define ratio, proportion, and proportional segments.

Quadrilaterals

  • Examine the properties of trapezoids.
  • Use the properties of special quadrilaterals.
  • Apply the properties of parallelograms.
  • Describe the characteristics of a quadrilateral.

Parallel Lines and Polygons

  • Identify different types of polygons and their components.
  • Define parallel lines, transversals, and angles.

Introduction to Trigonometry

  • Apply sine, cosine, and tangent to real-life problems.
  • Determine the area and perimeter of figures using trigonometry.
  • Define solving triangles.
  • Calculate the missing sides in a right triangle.
  • Identify the use of sine, cosine, and tangent in special right triangles.
  • Define the sine, cosine, and tangent of an acute angle.

Introduction to Analytic Geometry

  • Identify the slope of the line, point-slope form, and slope-intercept form of a line.
  • Calculate the length and midpoint of a line segment.
  • Define the Cartesian coordinate system.
  • Identify the relationship between geometry and algebra.

Foundations of Geometry

  • Construct perpendicular lines and angle bisector.
  • Formulate geometric proofs.
  • Describe segments, rays, and angles.
  • Identify points, lines, and planes.
  • Define deductive and inductive reasoning as well as proofs and axiomatic systems.

Circles

  • Construct a tangent to a circle and measure angles formed by tangents.
  • Describe the theorems of chords and secants of circles.
  • Define a circle and related terms.

Areas of Polygons and Circles

  • Apply the area formula to regular polygons.
  • Identify area and arc length of a sector.
  • Calculate the circumference and area of circles.
  • Determine areas of quadrilaterals.

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