Theme 1 basic drawing

TECHNICAL DRAWING I

THEME 2: BASIC PATHS IN THE PLANEBasic geometrics elements:

POINT:

A

B

C

No dimension.

It’s a position.

Always in CAPITAL letters.


LINE: It’s an addition of several points following the same direction.

Always in small letters; r, s, t…

r

r s

A

Two lines cut each other when they share

a point.

r

s

Two lines can be parallel when the

sharing point is in the infinite.

r

s

When the two lines share no point, they

cross each other.


HALF LINE: One point is known and the other is in the infinite. A point in the line defines tow half-lines, one to the left and the other to the right.

A

r∞ →

SEGMENT:

Ar

∞ →←∞

Is a kind of line defined between two known points.

A

r

B


CURVED LINE:

A curved line is a group of points constantly changing direction.

Always in small letters.


PLANE:

Is the set of points that arise when you move a straight line in one direction.We need the following information to define a plane:

A

B

C

Non aligned 3 points. Two lines cutting each other.

A

Two parallel lines.

A

A line and a point out of the line.

THEME 2: BASIC PATHS IN THE PLANELines within a plane:

● Bisecting line:


● To draw a perpendicular from “M” point outside the line:


● To draw a perpendicular from “P” point inside the line:


● To construct a perpendicular at the end of a given line:


● To draw parallel lines with the set squares:


● To draw perpendicular lines with the set squares:

THEME 2: BASIC PATHS IN THE PLANE

ANGLES:Is a measure of a turn. We use a protractor to measure an angle. Sometimes we use letters from Greek alphabet to name angles; α, β, γ, δ…And sometimes we name (B) the vertex of the angle and (choosing A and C points) on the two sides; we write ABC. So the angle reads ABC.

Different kind of angles:Null angle: α = 0°Acute angle: α < 90°Right angle: α = 90°Obtuse angle: α > 90°Plain angle: α = 180°Complete angle: α = 360°

Basic geometrics elements:


ANGLES:Two lines cutting each other at point O creates the following angles;

Basic geometrics elements:

Adjacent angles: α and β. Same vertex and side in common. Angles opposite at vertex; α and γ; β and δ.

So, α and γ / β and δ are of the same value.

α

βγ

δ


To construct an angle similar to a given angle;

Operations with angles :


Summing up angles;



Difference between angles;



To bisect an angle (bisector);



To bisect an angle (bisector);



Drawing angles;

60° angle: 90° angle:


15° angle: 75 ° angle:



Drawing angles;





The set of points having the same geometric characteristics.

1. Circumference:

2. Bisecting line:

Geometric places:


3. Bisector line:

4. The loci arc of a segment (depending on the angle):

Geometric places:


A circle is a plain figure bounded by a curved line called the circumference, witch is always equidistant from the centre.

Lines of a circumference:

● Radius; Any of the straight lines from the centre to the circumferences. The radius is half the diameter of the circumference.

● Diameter: The longest possible chord of a circumference. A line passing through the centre with both ends touching the circumference.

Circumference:


● Chord: A straight line, witch each end touching the circumference.

● Arrow; It’s a part of the radius between the chord and the circumference. The radius is perpendicular to the chord.

● Secant: A line that cuts the circumference at two points.

● Tangent: A line touching the circumference at one point. Forms a right angle with a radius of the circle. T is the point contact.

Circumference:

THEME 2: BASIC PATHS IN THE PLANECircumference:

THEME 2: BASIC PATHS IN THE PLANECircumference:

To construct a circumference when you have 3 points.

THEME 3: TRIANGLES, SQUARES AND REGULAR POLYGONSTRIANGLES:

· Is a polygon formed by three segments.

· The addition of every inner angles of a triangle is always 180º.

α + β + γ = 180º

· The value of the outside angle of a triangle is the addition of the two non-adjacent inside angles.

THEME 3: TRIANGLES, SQUARES AND REGULAR POLYGONSTRIANGLES:

· In every triangle, any side is always smaller than the addition of the other two;

a < b + c

· And any side is larger than the subtraction of the other two;

b > a - c

· In every triangle the larger angle is in front of the larger side;

c > a; γ > α

THEME 3: TRIANGLES, SQUARES AND REGULAR POLYGONSCLASSIFICATION OF TRIANGLES:

· Depending on sides;

· Equilateral: Isosceles: Scalene:

THEME 3: TRIANGLES, SQUARES AND REGULAR POLYGONSCLASSIFICATION OF TRIANGLES:

· Depending on angles;

· Acute:

· Right:

· Obtuse:

THEME 3: TRIANGLES, SQUARES AND REGULAR POLYGONSREMARKABLE LINES AND POINTS OF A TRIANGLE:

· Bisector / Incentre / Inscribed circle to a triangle.


· Bisecting line / Circumcentre / Circumscribed circle to a triangle.


· Altitudes / Orthocentre.


· Baricentre or Centre of Gravity.

THEME 3: TRIANGLES, SQUARES AND REGULAR POLYGONSCONSTRUCTING TRIANGLES:

a) Knowing the 3 sides a, b and c.

b) Knowing 2 of the sides and the angle between them.

c) Knowing one side, a, and the angles B and C.

THEME 3: TRIANGLES, QUADRILATERALS AND REGULAR POLYGONS

QUADRILATERAL:

· It is an polygon formed by 4 sides.

QUADRILATERALS

PARALELOGRAM (Two by two, sides

are parallel)

Trapezium (two sides are parallels,

the other two aren’t)

Trapezoid (no parallel sides)


QUADRILATERAL:

PARALELOGRAM (Two by two,

sides are parallel)

Square

Rectangle.

Rhombus.

Rhomboid


QUADRILATERAL:

Trapezium (two sides are parallels, the other

two aren’t)

Isosceles

Right

Scalene


QUADRILATERAL:

Trapezoid (no parallel sides)

Isosceles Scalene


REGULAR POLYGONS:

· What is a Polygon?

A closed plane figure made up of several line segments that are joined together.

The sides do not cross each other.

Exactly two sides meet at every vertex.


REGULAR POLYGONS:

· One polygon is regular if all the sides and all the angles are equal.

l = Side.a = Apotemer = Radiusα = 180º - (360º / n)λ = 360º / n


REGULAR POLYGONS:

· Regular Hexagon.


REGULAR POLYGONS:

· Regular triangle; equilateral triangle.


REGULAR POLYGONS:

· Dodecagon.


REGULAR POLYGONS:

· Square.


REGULAR POLYGONS:

· Octagon.


REGULAR POLYGONS:

· Pentagon


REGULAR POLYGONS:

· Decagon


REGULAR POLYGONS:

· Heptagon


REGULAR POLYGONS:

· General way.


REGULAR POLYGONS:

· Pentagon (knowing the the side)


REGULAR POLYGONS:

· Hexagon (knowing the the side)


REGULAR POLYGONS:

· Heptagon (knowing the the side)


REGULAR POLYGONS:

· Octagon (knowing the the side)


REGULAR POLYGONS:

· Nonagon, Enneagon (knowing the the side)


REGULAR POLYGONS:

· Decagon (knowing the the side)


REGULAR POLYGONS:

· General way (knowing the the side)

Education

Theme 1 basic drawing