AESTHETIC EDUCATION8th GRADE: Q1 / P1

TECHNICAL DRAWING:Technical drawing is a drawing or plan that is used to communicate direction and specifics to a group of people who are creating something, to explain how something works or how to build something.

Who Uses Technical Drawings Engineers Contractors Plumbers Electricians Landscape architects Inventors

An example of a technical drawing is a drawing made for a plumber with unique symbols to show where all the water lines, sinks, faucets, tubs and toilets are to be located. An example of a technical drawing is a drawing made with computer-assisted design (CAD) to show the details of a new home building project.

INSTRUMENTS:Drawing Board:

Drawing board is made from strips of well-seasoned soft wood generally 25 mm thick. One of the shorter edges of the rectangular board is provided with perfectly straight ebony edge which is used as working edge on which the T-square is moved while making Drawings.

T-square:

T-squares are made from hard wood. A T-square consists of two parts namely the stock and the

blade joined together at right angles to each other. The stock is made to slide along the working edge and the Blade moves on the Drawing board.

Set Squares:

Set squares are generally made from Plastic or celluloid material. They are triangular in shape with one corner, a right angle triangle. A pair of set squares (30°–60°) and 45°.

They are used to draw lines at 30°, 60° and 45° to the vertical and horizontal.

Protractor:

Protractors are used to mark or measure angles between 0 and 180°. They are semicircular in shape (of diameter 100mm) and are made of Plastic or celluloid . Protractors with circular shape capable of marking and measuring 0 to 360°

Drawing Pencils:

The accuracy and appearance of a Drawing depends on the quality of Pencil used to make Drawing.

The grade of a Pencil lead is marked on the Pencil.

HB denotes medium grade. Increase in hardness is shown by value put in front of H such as 2H, 3H etc.

Softer pencils are marked as B, 2B, and 4B etc.

Pencil marked 3B is softer than 2B and Pencil marked 4B is softer than 3B and so on.

Beginning of a Drawing may be made with H or 2H. For lettering and dimensioning, H and HB Pencils are used.

Drawing Pins and clips:

These are used to fix the Drawing sheet on the Drawing board.

Compass:

Compass is used for drawing circles and arcs of circles. The compass has two legs hinged at one end. One of the legs has a pointed needle fitted at the lower end whereas the other end has provision for inserting pencil lead.

Fineliner:

Fineliner pens are a class of fine fiber or plastic tip pens that are typically used for graphic, drawing or sketching purposes, but are also popular for handwriting as many people like the unique feel of the tip compared to a traditional ball-tipped pen.

The tips are generally long and metal-clad to allow use with rulers and templates without bending. Fineliners are generally relatively cheap, as the construction is very simple. They're mostly disposable, but there are a few premium refillable options. Most fineliner pens use dye-based ink, which is not hugely permanent, but there are many that use lightfast and waterproof pigment ink, especially the more technical drawing ranges.

AESTHETIC EDUCATION8th GRADE: Q1 / P1

TYPE OF LINES

A line is a series of points adjacent to each other. Where a point has no dimension, a line has one dimension. They have a length, but nothing else. In reality a line would need a second dimension to actually see it, but we’ll continue to call them lines and not something else here.

Lines are used to draw but they can also fill in spaces in a drawing and add texture.

We are going to make a small classification for the lines depending on a characteristic.

LINES BY THE POSITION IN THE SPACE:

LINES BY THE SHAPE THEY HAVE:

Note: there are more types of line by shape this is only a small list

LINES BY THEIR EXTENSION:

LINES BY THEIR RELATION WITH EACH OTHER:

WHAT IS AN ANGLE?

An angle is the amount of turn between two straight lines that have a common end point (the vertex).

AOB = is used to represent an angle.

A & B are the lines and O is the vertex.

TYPES OF ANGLES

Zero Angle: is the angle that measures 0º

AOB = 0º

Acute Angle: the measure of the angle is less than 90 °

AOB < 90º

Right Angle: is the angle that measures exactly 90 °

AOB = 90º

Obtuse Angle: the measure of the angle is greater than 90 °

AOB > 90º

Straight Angle: It is the angle that measures 180º

AOB = 180º

Reflex Angle: is one which is more than 180° but less than 360°

AOB > 180º AOB < 360º

Full Angle: It means turning around until you point in the same direction again or 360º

AOB = 360º

AESTHETIC EDUCATION

8th GRADE: Q1 / P2

A vertex is a corner. An edge is a line segment that joins two

vertices. A face is an individual surface.

TYPE OF TRIANGLES

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted △ A B C

A triangle has three sides and three angles The three angles always add to 180°

There are three special names given to triangles that tell how many sides (or angles) are equal.

There can be 3, 2 or no equal sides/angles:

Triangles can also have names that tell you what type of angle is inside:

AESTHETIC EDUCATION8th GRADE: Q1 / P2

PROTRACTOR USE:

Remember how one side of the angle traces out a circular arc? We use that circle to measure how big the angle is. We look at how much the angle has “opened” as compared to the full circle.

Angles are measured in degrees. The symbol for degrees is a little circle °.

The FULL CIRCLE is 360° (360 degrees). A half circle or a straight angle is 180°. A quarter circle or a right angle is 90°.

Show the angles below using two pencils. Try to “see” the circle that is traced out in the air.

An obtuse angle; 127°

A right angle; 90°

How to measure an angle with a protractor:

Place the midpoint of the protractor on the VERTEX of the angle.

Line up one side of the angle with the zero line of the protractor (where you see the number 0).

Read the degrees where the other side crosses the number scale.

Take care to read from the right set of numbers. A protractor has two sets of numbers: one set goes from 0 to 180, the other set from 180 to 0. Which one you read depends on how you place the protractor: place it so that one side of the angle lines up with one of the zeros, and read that set of numbers.

In the examples above we lined up the one side of the angle with the zero of the lower set of numbers, so we need to read the lower set of numbers.

1. Measure the angles. Label each angle as acute or obtuse.

a.  __________° ________________

b.  __________° ________________

c.  __________° ________________

d.  __________° ________________

AESTHETIC EDUCATION8th GRADE: Q1 / P2

Draw Triangles Using a Ruler and a Protractor

How can we draw a specific triangle?

We can draw a triangle using a ruler and a protractor. Remember in the last lesson that a protractor is used to measure angles. We can use the protractor to figure out the measure of an angle and then draw in the rest of the triangle with the ruler.

Also remember: The three angles always add to 180°

So if the triangle has:

Angle A: 50 You need to add the angles thatAngle B: 60 you already know and thenAngle C: ? subtract it from 180º

Angle A + Angle B = 110º

180º - 110º = Angle C

ANGLE C = 70º

To draw a triangle you only need two angles and a baseline. Later you will see others ways to do it, but for now we will learn this one.

Angle A= 50º Angle B= 60ª Angle C= ______

Step 1:Draw the base line and mark each vertex.

Step 2:Place the protractor correctly at vertex A to measure the angle A. Then using a ruler draw a line of any extension.

Step 3:Repeat the same procedure from B, using the angle B.Draw a line and make sure the new line intersects the previously drawn line.

Step 4:You can check with the protractor that the angle C will be the same to the one you found doing the math.

AESTHETIC EDUCATION8TH GRADE: Q1P3Materials: A4 white paper, pencil, protractor, ruler, set squares and eraser.

JUST TO RECALL

WHAT IS A VERTICAL LINE?

A vertical line is one that goes straight up and down, and has no slope.

WHAT IS A HORIZONTAL LINE?

A horizontal line is one that goes from left-to-right and has a slope of zero.

WHAT IS A LEANING LINE?

A leaning line is a sloping or slanting line, is not horizontal nor vertical.

NOTE: The slope of a line (also called the gradient of a line) is a number that describes how "steep" it is.

WHAT ARE PARALLEL LINES?

Lines are parallel if they are always the same distance apart (called "equidistant"), and will never meet. (They also point in the same direction).

WHAT IS AN ANGLE?

An angle is the amount of turn between two straight lines that have a common end point (the vertex).

The angles we are going to be using more often:

Acute Angle: the angle is less than 90 °

Right Angle: an angle that measures exactly 90 °

Obtuse Angle: the angle is greater than 90 °

QUADRILATERALS

GOALS Identify the angles and how to properly use the protractor and ruler to correctly build the different four sided figures.

Short overview on this topic:

What are the QUADRILATERALS?The quadrilaterals are figures or polygons that have four sides, four angles and four vertices.

Example of them:

Square, Rectangle, Parallelogram, Rhombus, and there are other two that we are going to know just a bit of them, they are the Trapezoid and the kite.

QUADRILATERALS

Quadrilateral just means "four sides" (Quad means four, lateral means side).

A Quadrilateral has four-sides, it is 2-dimensional (a flat shape), closed (the lines join up), and has straight sides.

Quadrilaterals are simple (not self-intersecting) or complex (self-intersecting), also called crossed. Simple quadrilaterals are either convex or concave.

DO NOT GET CONFUSED! Here we are only going to see the simple convex quadrilaterals.

The interior angles of a simple (and planar) quadrilateral ABCD add up to 360 degrees, that is∠ A + ∠ B + ∠ C + ∠ D = 360º

This is a special case of the n-gon interior angle sum formula (n − 2) × 180°.

Sometimes, the term quadrangle is used, by analogy with triangle, and sometimes tetragon for consistency with pentagon (5-sided), hexagon (6-sided) and so on.

Simple quadrilaterals

Any quadrilateral that is not self-intersecting is a simple quadrilateral.

Simple CONVEX quadrilaterals

In a convex quadrilateral, all interior angles are less than 180° and the two diagonals both lie inside the quadrilateral.

Simple CONCAVE quadrilaterals

In a concave quadrilateral, one interior angle is bigger than 180° and one of the two diagonals lies outside the quadrilateral.

A dart (or arrowhead) is a concave quadrilateral with bilateral symmetry like a kite, but one interior angle is reflex.

SQUARE (Regular quadrilateral)All four sides are of equal length (equilateral), and all four angles are right angles. Also opposite sides are parallel.

RECTANGLEA rectangle is a four-sided shape where every angle is a right angle (90°).

Also opposite sides are parallel and of equal length.

RHOMBUSA rhombus is a four-sided shape where all sides have equal length.

Also opposite sides are parallel and opposite angles are equal.

Another interesting thing is that the diagonals (dashed lines in second figure) meet in the middle at a right angle. In other words they "bisect" (cut in half) each other at right angles.

A rhombus is sometimes called a rhomb or a diamond.

PARALLELOGRAMA parallelogram has opposite sides parallel and equal in length. Also opposite angles are equal (angles "a" are the same, and angles "b" are the same).

Notice that angle a + b add up to 180º

NOTE: Squares, Rectangles and Rhombuses are all Parallelograms!

Example:

A parallelogram with: all sides equal and angles "a" and "b" as right angles is a square!

FOR YOU TO KNOW

TRAPEZOIDA trapezoid has a pair of opposite sides parallel.

It is called an Isosceles trapezoid if the sides that aren't parallel are equal in length and both angles coming from a parallel side are equal, as shown.

And a trapezium is a quadrilateral with NO parallel sides:

Trapezoid Trapezium

a pair of parallel sides NO parallel sides

KITEHey, it looks like a kite. It has two pairs of sides.

Each pair is made up of adjacent sides (they meet) that are equal in length.

The angles are equal where the pairs meet. Diagonals (dashed lines) meet at a right angle, and one of the diagonal bisects (cuts equally in half) the other.

Irregular QuadrilateralsThe only regular quadrilateral is a square. So all other quadrilaterals are irregular.

AESTHETIC EDUCATION8TH GRADE: Q1P3Materials: A4 white paper, pencil, protractor, ruler, set squares and eraser.

REGULAR POLYGONSA polygon is a plane shape (two-dimensional) with straight sides.

Examples: include triangles, quadrilaterals, pentagons, hexagons and so on.

A regular polygon is a polygon that is:

Equiangular (all angles are equal in measure) and Equilateral (all sides have the same length).

Otherwise it is irregular.

The most important elements of a regular polygon are: Center, Radius, Side, vertex, and Apothem

Side: one of the line segments that make up the polygon.

Vertex: each angular point of a polygon, polyhedron, or other figure.

Radius: a straight line from the center to one vertex

Apothem: a line from the center of a regular polygon to the midpoint of one of its sides.

Center: the middle point of the regular Polygon.

Interior Angle: Angle formed by two adjacent sides inside the polygon.

Exterior Angle: Angle formed by two adjacent sides outside the polygon.

"Circumcircle, Incircle, Radius and Apothem ..."

They are just the names of the "outer" and "inner" circles (and each radius) that can be drawn on a polygon like this:

The "outside" circle is called a circumcircle, and it connects all vertices (corner points) of the polygon.

The radius of the circumcircle is also the radius of the polygon.

The "inside" circle is called an incircle and it just touches each side of the polygon at its midpoint.

The radius of the incircle is the apothem of the polygon.

Regular Polygons

Regular Pentagon5 sidesInterior angle 108º

Regular Hexagon6 sidesInterior angle 120º

Regular Heptagon 7 sidesInterior angle 128.57°

Regular Octagon8 sidesInterior angle 135°

Regular Nonagon9 sidesInterior angle 140°

Regular Decagon 10 sidesInterior angle 144º

FOR YOU TO KNOW:

POLYGON NAMESgenerally accepted names

Sides Namen N-gon3 Triangle4 Quadrilateral5 Pentagon6 Hexagon7 Heptagon8 Octagon10 Decagon12 Dodecagon

Names for other polygons have been proposed.

Sides Name9 Nonagon, Enneagon 11 Undecagon, Hendecagon13 Tridecagon, Triskaidecagon14 Tetradecagon, Tetrakaidecagon15 Pentadecagon, Pentakaidecagon16 Hexadecagon, Hexakaidecagon17 Heptadecagon, Heptakaidecagon18 Octadecagon, Octakaidecagon19 Enneadecagon, Enneakaidecagon20 Icosagon30 Triacontagon40 Tetracontagon50 Pentacontagon60 Hexacontagon70 Heptacontagon80 Octacontagon90 Enneacontagon100 Hectogon, Hecatontagon1,000 Chiliagon10,000 Myriagon

To construct a name, combine the prefix+suffix

Sides Prefix

20 Icosikai...30 Triacontakai...

40 Tetracontakai...50 Pentacontakai...

60 Hexacontakai...70 Heptacontakai...

80 Octacontakai...90 Enneacontakai...

+

Sides Suffix

+1 ...henagon+2 ...digon

+3 ...trigon+4 ...tetragon

+5 ...pentagon+6 ...hexagon

+7 ...heptagon+8 ...octagon

+9 ...enneagonExamples: 46 sided polygon – Tetracontakaihexagon 28 sided polygon - Icosikaioctagon

However, many people use the form n-gon, as in 46-gon, or 28-gon instead of these names.

HOW TO CALCULATE THE INTERIOR AND EXTERIOR ANGLE OF A REGULAR POLYGON?

HOW TO DRAW A REGULAR POLYGON?