## MTH 156 - Elementary Geometry

### Course Description

Effective: 2018-01-01

Presents the fundamentals of plane and solid geometry and introduces non-Euclidean geometries and current topics.

Lecture 3 hours. Total 3 hours per week.

3 credits

### General Course Purpose

To present the fundamentals of plane and solid geometry and introduce non-Euclidean geometries and current topics while modeling sound pedagogy to support students in presenting these concepts to their own students

### Course Prerequisites/Corequisites

Prerequisite: MTE 1-9 or placement.

### Course Objectives

- Basic Properties, Definitions, Symbols, and Proof
- Demonstrate geometric properties: intersecting lines, shortest distance between a point and a line, congruence of vertical angles, the seven basic Euclidean constructions, the polygon sum formula, the relationships between the base angles of an isosceles triangle and between its legs, intersecting planes, congruent segments, congruent angles, and congruent polygons
- Understand relevant geometry terminology
- Recognize relevant conventional geometric symbols
- Use definitions and postulates in two-column (deductive) proofs to prove basic theorems
- Apply properties learned to solve problems
- Properties of Quadrilaterals, Circles, and Congruent Triangles
- Demonstrate geometric properties: relationships between sides, angles, and diagonals of parallelograms, relationships between diagonals in rhombi and in rectangles, relationships between special angles, arcs, chords, secants, and tangents in circles, and conditions sufficient to prove or dispute congruence of triangles
- Understand relevant geometry terminology
- Recognize relevant conventional geometric symbols
- Use definitions, postulates, and proven theorems to prove triangles congruent in two-column proofs
- Apply properties learned to solve problems
- Transformations, Symmetry, and Area
- Demonstrate, investigate, and discover geometric properties using inductive reasoning: basic transformations including translations, rotations, reflections, two reflections over parallel lines and two reflections over intersecting lines, distances between relevant points and lines in these transformations, numbers of reflection symmetries of regular polygons and numbers and degrees of the rotational symmetries of regular polygons, formulae for the areas of parallelograms, triangles, trapezoids, and circles
- Demonstrate understanding of relevant geometry terminology
- Recognize relevant conventional geometric symbols
- Apply properties learned to solve problems

### Major Topics to be Included

- Basic Properties, Definitions, Symbols, and Proof
- Properties of Quadrilaterals, Circles, and Congruent Triangles
- Transformations, Symmetry, and Area
- Theorem of Pythagoras, Solid Geometry, Non-Euclidean Geometries and Topology