-Bisector line of the segment -Bisector line of the angle -Proportionality, Thales theorem, scale factor -Homothetic transform (applied to segments and circumferences) -Conical curves -Exercises related with the previous topics Definition, basic properties and representation of: - Translation - Axial symmetry - Rotation Product of movements Exercises Study the following topics related with triangles: -Sum of internal angles. -Definitions and properties of: circumcentre, orthocentre, incentre/execentres, centroid -Similarity of triangles, leg's / height / pythagoras / generalised pythagoras tehorems -Exercises on the basic construction of triangles -Definition of the regular polygons -Property of the sum of interior/exterior angles -Definition and classification of quadrilaterals -Basic properties of the parallelogram and trapezium -Exercices on the construction of basic quadrilaterals by means of locus intersection, triangles, or movements -Definitions and basic properties of a circumference. -Properties of the chords. -Tangent lines -Angles on the circumference: central, inscribed, semi-inscribed, internal, external. And their properties and relations. -Arco capaz. -Exercises on tangent -Exercises with the circumference angles and arco capaz

Specific Objectives

1.- Learn to make the proposed geometric constructions and understand their basic properties. 2.- Put into practice the theoretical knowledge. 3.- Acquire skills when drawing two-dimensional geometric figures. 4.- Become familiar with the use of drawing tools such as the compass or curve templates (and the like). 5.- Learn to solve simple geometric problems. Learn basic concepts of movements, properties, representation and composition. Learn basic properties of triangles and solve basic exercises. Learn properties of polygons and solve basic exercises Know basic properties of the circumference and its angles

Dedication

Definition of orthographic projection (American and European). Exercises related to the orthographic projection. In general, a projection direction and a figure will be given and the view of the figure demanded. Exercises where some transformation is applied to the figure (rotations) will be considered.

Specific Objectives

1.1.- Understand the concept of "projection on a plane". 1.2.- Know various ways of making these projections. 1.3.- Know the dihedral projection system. 1.4.- Become familiar with the concepts of: plan, elevation, profile. 1.5.- Know how to correctly position each of the views or projections in both the American and European systems. 1.6.- Differentiate between edge / face and hidden face. 1) Learn to make orthographic projections of a piece; 2) Ability to see a piece that moves in space (imagine the piece in the final position when the initial position and a movement are defined); 3) To be familiar with different figure typologies. Pieces with curved faces will be considered; 4) Being able to imagina a sectioned piece.

Dedication

Basic theoretical indications on free prospects. Free view and interpretation of pieces. Opposite view and perspectives from a certain point of view. Basic points: - Basic rules of freehand drawing: parallelism, proportionality - Basic tips for making a freehand drawing: orientation of the appropriate axes, wire structures etc - Drawing of simple figures - Concept of elevation direction vs. observer's point of view - Drawing figures from a certain point of view. - 8 positions in space -Opposite view - Figures with curved faces - Exercises Session dedicated to solving the unit's own exercises, and exam problems from previous courses

Specific Objectives

Assimilate the concept of one-piece free perspective and learn the basic tips. 1.1.- Acquire enough spatial vision to imagine a piece, given its dihedral projections 1.2.- Acquire enough freehand drawing skills to make an intelligible drawing 1.3.- Be able to draw a free perspective respecting aspects such as parallelism and proportionality. 1.4.- Ability to imagine the opposite view of a piece, known its direct view. 1.5.- Ability to imagine what an observer located at any point in space sees.

Dedication

GD_1. System elements; The point. 1.1 System elements definition. 1.2 Point representation. 1.3 Coordinate axes. 1.4 Identification of a point by its coordinates. 1.5 Different positions of the point - Point at 1st dihedral. - Point at 2nd dihedral. - Point at 3rd dihedral. - Point at 4 ° dihedral. - Point in the 1st bisector. - Point in the 2nd bisector. - Point in the vertical plane. - Point in the horizontal plane. - Point at the ground line. GD_2. The straight line. 2.1 Stright line's representation. 2.2 Point contained in a line. 2.3 Traces of a line. 2.4 Line defined by two points. 2.5 Intersection of two lines. 2.6 Parallel lines. Parallel stright line by a point to another one. 2.7 Relative straight line's positions. - Horizontal straight line. - Front straight line. - Parallel strainght line to the ground line. - Vertical straight line. - Edge straight line.. - Straight line contained in the 1st bisector. - Straight line contained in the 2nd bisector. 2.8 straight line's views: hidden and views parts. 2.9 Straight line profile. 2.10 Profile plane abatement and profile plane disabatement. 2.11 Straight profile lines' intersection. 2.12 Parallel line to a profile lines passing by a determinate point. GD_3. The plane. 3.1 Plane's representation. 3.2 Plane's points. Horizontal projection of a known point vertical projection or vice versa. 3.3 Straight line contained in a plane. 3.4 Straight lines individuals contained in a plane. - Front straight line. - Horizontal straight line. - Maximum slope straight line. - Maximum tilt straight line. 3.5 Plane's particular positions. - Vertical plane. - Edge plane. - Flat plane. - Horizontal plane. - Frontal plane. - Parallel plane to the ground line. - A plane that passes through the ground line. - Perpendicular plane to the 1st bisector. - Perpendicular plane to the 2nd bisector. 3.6 Traces of a plane defined by two lines. 3.7 Types of planes defined by a straight line. - Vertical plane. - Edge Plane. - Parallel plane to the ground line.. - Perpendicular plane to the 1st bisector. - Perpendicular plane to the 2nd bisector. GD_4. Parallelism and perpendicularity 4.1 Parallel planes. 4.2 Parallel straight line to a plane by a point.. - General case. - Plane parallel to the ground line. - Plane passing through the ground line. - Parallel straight line to a plane by a point. - Parallel plane to two given straight lines by a point. - Parallel straight line by a point to a plane which is built by a given straight line. - Straight line supported in two ones' by a point. - Straight line supported in two ones' by a given direction. 4.3 Theorem of the three perpendicular. 4.4 Perpendicular line to a plane passing by a point: - General case. - Perpendicular plane to the ground or passing through the ground line. - Perpendicular plane to the bisectors. 4.5 Perpendicular plane to a line passing by a point. 4.6 Perpendicular straight line to other two ones. Common perpendicular. 4.7 Perpendicular plane to two ones: - Straight line's projections on a plane. - Orthogonal straight line to a given one which is build on another by a point. - Straight line contained in a plane which is perpendicular to another one by a defined plane point. - Straight line which is perpendicular and parallel to two differents planes by a point. Session dedicated to solving the unit's own exercises, and exam problems from previous courses

Specific Objectives

1.1.- Be able to deduce and transfer from three-dimensional space to two-dimensional space using the dihedral system, and restore from dihedral projections to three-dimensional space. 1.2.- Represent three-dimensional solids and their basic geometric elements that make it up: points, lines and planes. 1.3.- Know the basic positions of the line and the plane. 1.4.- Determine the relative positions between the different geometric elements: points, lines and planes. 1.5.- Determine the conditions of membership of said elements. 1.6.- Learn to use the terminology of the dihedral system with fluency and solvency. 3.3.- Construction using operating methods of the subtraction dihedral system and parallel planes between them and others. 3.3.- Understanding and using the theorem of the three perpendiculars for their use in the construction of perpendicular lines between them, perpendicular lines with planes, and perpendicular planes between them.

Dedication

Definition of the dimensioned plane system. - Representation of points, lines and planes. - Basic operations: Parallelism, perpendicularity and distances Representation and concept of: - Use of scales. Graphic scale. - Concept of contour (horizontal plane) - Geometric Surfaces - Point curves in space - Definition of the basic elements that are part of a roof and description of what it is to solve the problem of a roof with bounded planes. Application of the concept of scale and equidistance to dimensioned plane problems. - Initial cover exercises. Session dedicated to solving the unit's own exercises, and exam problems from previous courses -Representation of land -Characteristic elements of the orography -Long profile. Constant slope path and maximum slope path. -Cross section: concept of cut and fill. -Transition surfaces: cases with zero slope contours -Platform exercises Session dedicated to solving the unit's own exercises, and exam problems from previous courses Definition of linear work. Cut and fill concepts. Definition of the type of surface that is formed in the cuttings and embankments of a linear work depending on the type of plan layout (straight, circular or curved) and whether it is a section with zero or constant slope. Session dedicated to solving the unit's own exercises, and exam problems from previous courses

Specific Objectives

1.1.- Learn the basic principles of the Bounded Plans. 1.2.- Know how points and lines are represented. 1.3.- Acquire the most basic skills to carry out small operations related to points and lines (example: placing a point on a line; determining the distance between two points). 1.4.- Know how a plane is represented. 1.5.- Become familiar with concepts such as "maximum slope line", "trace of the plane", ... 1.6.- Learn to perform geometric operations that include planes (intersection of two planes, draw a line contained in a plane, ... 1.7.- Know how to draw planes and lines that are parallel and perpendicular 1.8.- Be able to do other three-dimensional geometric operations such as intersecting a line with a plane, collapsing planes, drawing planes and lines that form a given angle with another plane etc. 2.1.- Learn how to represent basic geometric surfaces (spheres, cones, cylinders) using dimensioned planes. 2.2.- Learn the name of basic elements of a roof. 2.3.- Understand what the definition of a roof consists of through dimensioned plans. 2.4.- Be clear about what the problem data may be and what results can be asked of us. 2.5.- Know how to determine a roof (level and intersection curves of each of the parts that form it), fixed: the outer contour, the type of surface that forms it and its geometric characteristics, the scale of the exercise and the equidistance of job. 2.6.-Know how to determine a roof (level lines and intersection of each of the parts that form it), fixed: the outer contour, the type of surface that forms it and its geometric characteristics, the scale of the exercise and the equidistance of job. 3.1.- Know the concept of platform. 3.2.- Know the concept of "cut" and "embankment" and in which cases we find each one of them. 3.3.- Know how to determine the surfaces generated in the construction of a platform as well as its intersection with the ground. Geometric interpretation of the results obtained. 4.1.- Know the concept of linear work. 4.2.- Know the concept of "clearing" and "embankment" and in which cases we find each of them. 4.3.- Know how to determine the type of cut or embankment surface that we will have to draw based on the plan layout or elevation of a linear work. 4.4.- Learn the "profile method". 4.5.- Know how to determine the surfaces generated in the construction of a platform or a linear work as well as its intersection with the ground. Geometric interpretation of the results obtained

Dedication

1. Introduction. Description of the system. 2.- Basic tools for 2D design: drawing. - Exercises 3.- Basic tools for 2D design: editing. - Exercises 4.- Management tools: layers, properties and elements. - Exercises 5.- Blocks and attributes. 6.- Dimensions and text. - Exercises 7.- Paper space configuration. Windows, views and scales. 8.- Configuration for printing plans. - Application to exercises 9.- Introduction to 3D space: work plans and views. - Exercises 10.- Creation of primitive solids. 11.- Boolean operations with solids. - Exercises 12.- Editing and transformations of 3D solids. - Exercises 13.- Views and perspectives with 3D solids - Exercises

Specific Objectives

The objectives of the CAD laboratory are: - Preparation of students for the use of computer instruments as a tool in solving geometric problems. - Identify and represent through the system of multiple, axonometric and conical views, the characteristics of bodies, surfaces and objects, according to their location in space. - Know, identify, represent and use the known surfaces and volumes in geometry using proprietary engineering software applied to projects. - Application of current computer tools to graphic representation in the field of Civil Engineering through the use of vector-assisted design programs. - Introduction of the student in the rational use of computing as a work base, under the "interface" of the operating systems, and the application of specific vector software as a 2D and 3D drawing tool. Always under the conceptual guideline of the geometric structuring of the projects to be represented and the help of informatics in the field of descriptive geometry and technical drawing.

Dedication

Dedication

Session dedicated to resolving doubts openly. It will typically be held on the days before the assessments. Completion of practical exercises in class. Performing virtual tests.

Specific Objectives

Answer doubts and solve exercises Complement the continuous assessment note. Fix theoretical concepts. Receive information before the partial assessments.

Dedication

Course days that are affected by a public holiday

Dedication