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. To enroll, speak with an Enrollment Advisor.

Topics and Objectives

Areas of Polygons and Circles
- Determine areas of quadrilaterals.
- Calculate the circumference and area of circles.
- Identify area and arc length of a sector.
- Apply the area formula to regular polygons.
Circles
- Define a circle and related terms.
- Describe the theorems of chords and secants of circles.
- Construct a tangent to a circle and measure angles formed by tangents.
Foundations of Geometry
- Define deductive and inductive reasoning as well as proofs and axiomatic systems.
- Identify points, lines, and planes.
- Describe segments, rays, and angles.
- Formulate geometric proofs.
- Construct perpendicular lines and angle bisector.
Introduction to Analytic Geometry
- Identify the relationship between geometry and algebra.
- Define the Cartesian coordinate system.
- Calculate the length and midpoint of a line segment.
- Identify the slope of the line, point-slope form, and slope-intercept form of a line.
Introduction to Trigonometry
- Define the sine, cosine, and tangent of an acute angle.
- Identify the use of sine, cosine, and tangent in special right triangles.
- Calculate the missing sides in a right triangle.
- Define solving triangles.
- Determine the area and perimeter of figures using trigonometry.
- Apply sine, cosine, and tangent to real-life problems.
Parallel Lines and Polygons
- Define parallel lines, transversals, and angles.
- Identify different types of polygons and their components.
Quadrilaterals
- Describe the characteristics of a quadrilateral.
- Apply the properties of parallelograms.
- Use the properties of special quadrilaterals.
- Examine the properties of trapezoids.
Similar Polygons and the Pythagorean Theorem
- Define ratio, proportion, and proportional segments.
- Apply the postulates and theorems of similar polygons.
- Construct proportional segments of polygons.
- Demonstrate the applications of the Pythagorean Theorem.
Solid Geometry
- Identify the behavior of lines and planes in space.
- Define solid figures that form in space.
- Calculate the surface area and volume of prisms, pyramids, cylinders, cones, and spheres.
Triangles
- Classify triangles by their sides and angles.
- Use geometric theorems to prove how triangles are congruent.
- Construct a triangle congruent to a given triangle.
- Use congruent and right triangles to prove statements and theorems.
- Construct triangles including altitude and the median parts.

The University of Phoenix reserves the right to modify courses.
While widely available, not all programs are available in all locations or in both online and on-campus formats. Please check with a University Enrollment Advisor.
Transferability of credit is at the discretion of the receiving institution. It is the student’s responsibility to confirm whether or not credits earned at University of Phoenix will be accepted by another institution of the student’s choice.

Geometry –

mth432

Areas of Polygons and Circles

Circles

Foundations of Geometry

Introduction to Analytic Geometry

Introduction to Trigonometry

Parallel Lines and Polygons

Quadrilaterals

Similar Polygons and the Pythagorean Theorem

Solid Geometry

Triangles

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