At the end of this course the student will have acquired knowledge and skills that will enable him:
To know and understand some of the principal results on the Euclidean
To develop skills to solve geometric problems and no systematic ones
To be able to visualize in the space

General characterization





Responsible teacher

Ana Cristina Malheiro Casimiro


Weekly - 4

Total - 70

Teaching language



Available soon


"Foundations of Geometry" (2nd edition), Gerard A. Venema, 2006, Pearson

“Curso de Geometria”, Paulo Ventura Araújo, Trajectos Ciência, 1998, Gradiva

"A course in Modern Geometries" (2nd edition), Judith N. Cederberg, 2001, Undergraduate Texts in Mathematics, Springer

“Geometry and symmetry”, L. Christine Kinsey, T. E. Moore, E. Prassidis 2011, John Wiley and Sons

“Geometry, ancient and modern”, J.R. Silvester, 2001, Oxford Univ. Press

“Axiomatic Geometry”, John M. Lee, 2013, American Mathematical Society

“Continuous Symmetry From Euclid to Klein”, W. Barker e R. Howe, 2007, American Mathematical Society

Teaching method

There are classes in which theory is lectured and illustrated by examples. There are also problem solving sessions. Some exercises are left to the students to be solved on their own as part of their learning process. Students can ask questions during the classes, in weekly scheduled sessions or in special sessions accorded directly with the professor. There is a mid evaluation that can substitute the final exam in case of approval. Otherwise the student must pass the final exam. In order to be evaluated, students must attend, at least, 2/3 of the lectures.

Evaluation method

Geometry - 2023/2024

Evaluation Rules

Students enrolled for the first time in the unit must attend all classes, except up to 3 lectures.

Students that have already been enrolled in the unit must attend, at least, 2/3 of the lectures.

The students that do not fulfill the above requirements automatically fail "Geometria". 

Subject matter

1. Axiomatic geometry: introduction, incidence geometry, axioms for plane geometry, angles, triangles, models of neutral geometry (cartesian model, Poincaré disk model), parallel axiom (equivalence with the sum of the inner angles of a triangle is 180º).

2. Straightedge and compass constructions: basic constructions, construction of regular polygons, impossible constructions.

3. Groups of transformations in the plane and in the Euclidean space: affinities, similarities and isometries and its classification

4. Non Euclidean geometries: models of the projective or elliptic or hyperbolic planes (to choose one of the 3 geometries)