MATH 1453: Geometry

Download as PDF
Subject:
Mathematics
Credit hours: 3 Lecture hours: 3 Lab hours: 0
PCS code (Local ID):
Remedial Education
View Class Schedule
Course Description

The student will use inductive, deductive, and indirect proofs in the study of plane and solid geometry, properties of congruence, similarity, ratio and proportion, area, perimeter, and volume of basic figures.

Prerequisite(s)

MATH 1424 with a grade of C or better

Topical Outline
  1. Intro to Geometry
    1. Points, lines, planes
    2. Segments, angles and their measure
    3. Angle pairs and their relationships
    4. Basic formulas
    5. Basic constructions
  2. Introduction to Reasoning and Proofs
    1. Perimeter, circumference, and area
    2. Inductive and deductive reasoning
    3. Conditional statements
    4. Proving theorems about angles
  3. Parallel and Perpendicular Lines
    1. Lines, angles and transversals
    2. Proving theorems about parallel and perpendicular lines
    3. Constructions
    4. Coordinate geometry
  4. Triangles and Congruence
    1. Types of triangles
    2. SSS, SAS, ASA, AAS
    3. Proofs using congruent triangles
  5. Special Properties of Triangles
    1. Bisectors, medians, and altitudes of triangles
    2. Indirect proofs
  6. Quadrilaterals
    1. Polygons, parallelograms, rhombuses, rectangles, squares, trapezoids, and kites
    2. Proofs using quadrilaterals
  7. Similarity
    1. Ratios and proportions
    2. Proportion properties
    3. Similar polygons
    4.  Proving triangles similar
  8. Area
    1. Angle measures of polygons
    2. Areas of triangles, quadrilaterals, and regular polygons
    3. Arc measures, circumferences and arc lengths of circles
    4. Areas of circles and sectors

At the end of this course, students will be able to:

  • Use inductive and deductive reasoning to establish the validity of an argument.
  • Construct proofs of basic geometric theorems.
  • Apply properties of geometric figures to solve for unknown values.
  • Perform basic constructions.
  • Apply formulas to solve problems related to perimeter, area, and volume.
  • Solve applications related to parallel and perpendicular lines.
  • Use Pythagorean Theorem to solve applications.
  • Solve applications involving circles.
  • Solve problems involving congruency and similarity.