Module: Geometry

Latest Module Specifications

Current Academic Year 2025 - 2026

Module Title	Geometry
Module Code	MTH1049 (ITS: MS302)
Faculty	Mathematical Sciences	School	Science & Health
NFQ level	8	Credit Rating	7.5

Description

This module focusses on the axiomatic approach to Euclidean geometry, paying particular attention to the role of this topic in the Irish second level mathematics syllabus. Non-Euclidean geometry will also be studied and students will use dynamic geometry software in the module.

Learning Outcomes

1. Describe the roles of defined, undefined and implicitly defined terms, axioms, lemmas, theorems and corollaries in a system of geometry.
2. Present proofs and constructions in Euclidean and non-Euclidean geometry
3. Solve problems in Euclidean geometry and plane trigonometry.
4. Describe applications and manifestations of geometry in the natural and man-made world.
5. Use dynamic software in teaching geometry.

*Type*	*Hours*	*Description*
Workload	Full time hours per semester
Lecture	24	Two lectures each week
Tutorial	12	One tutorial/problem session each week
Independent Study	139.5	No Description
Laboratory	12	Geogebra sessions in the computer lab.
Total Workload: 187.5

Section Breakdown
CRN	11215	Part of Term	Semester 1
Coursework	0%	Examination Weight	0%
Grade Scale	40PASS	Pass Both Elements	Y
Resit Category	RC1	Best Mark	N
Module Co-ordinator	Marco Viola	Module Teacher	Louise Nolan, Thorsten Neuschel

Type	Description	% of total	Assessment Date
Assessment Breakdown
In Class Test	n/a	7.5%	Week 6
In Class Test	n/a	7.5%	Week 10
Assignment	Series of assignments using the Geogebra software package.	10%	As required
Formal Examination	End-of-Semester Final Examination	75%	End-of-Semester

Reassessment Requirement Type
Resit arrangements are explained by the following categories; RC1: A resit is available for both^* components of the module. RC2: No resit is available for a 100% coursework module. RC3: No resit is available for the coursework component where there is a coursework and summative examination element. ^* ‘Both’ is used in the context of the module having a coursework/summative examination split; where the module is 100% coursework, there will also be a resit of the assessment

Pre-requisite	None
Co-requisite	None
Compatibles	None
Incompatibles	None

All module information is indicative and subject to change. For further information,students are advised to refer to the University's Marks and Standards and Programme Specific Regulations at: http://www.dcu.ie/registry/examinations/index.shtml

Indicative Content and Learning Activities

The terms and axioms of Euclidean geometry

Topics in Euclidean geometry
a. Length, distance, angles and angle measure b. Equivalent characterisations of congruent triangles c. Parallel and perpendicular lines; parallelograms and quadrilaterals d. Ratios and similarity e. Area and Pythagoras’s theorem f. Circles and special triangle points

Constructions in Euclidean geometry

Applications of Euclidean geometry

Non-Euclidean geometries

Using Geogebra

Indicative Reading List

Books:

Department of Education and Skills: 0, Geometry for School Mathematics (Section B, Leaving Certificate Mathematics Syllabus),

Articles:
None

Other Resources

None