AESTHETIC EDUCATION10th 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 EDUCATION10th 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

10th GRADE: Q1 / P1

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 EDUCATION10TH GRADE: Q1P1

CLASSIFICATION OF ANGLES BY THE POSITION THEY KEEP BETWEEN EACH OTHER.

NOTE: Congruent AnglesCongruent Angles have the same angle (in degrees or radians). That is all.

1. Complementary Angles.

Two angles are Complementary when they add up to 90 degrees (a Right Angle).These two angles (40° and 50°) are Complementary Angles, because they add up to 90°:

Notice that together they make a right angle.But the angles don't have to be together.These two are complementary because 27° + 63° = 90°

2. Supplementary Angles

Two Angles are Supplementary when they add up to 180 degrees.

These two angles (140° and 40°) are Supplementary Angles, because they add up to 180°:

Notice that together they make a straight angle.But the angles don't have to be together.

3. Corresponding Angles

When two parallels lines are crossed by another line (called the Transversal):The angles in matching corners are called Corresponding Angles and are equal.

a = e b = f c = g d = h

4. Alternate Interior Angles

When parallels lines are crossed by another line (called the Transversal):The pairs of angles on opposite sides of the transversal but inside the parallels lines are called Alternate Interior Angles and are equal.

c = f d = e

5. Alternate Exterior Angles.

When parallel lines are crossed by another line (called the Transversal):The pairs of angles on opposite sides of the transversal but outside the parallel lines are called Alternate Exterior Angles and are equal.

a = h b = g

6. Vertically Opposite Angles

Vertically Opposite Angles are the angles opposite each other when two lines cross.

NOTE: "Vertical" in this case means they share the same Vertex (or corner point), not the usual meaning of up-down.

In this example, a° and b° are vertically opposite angles.

The interesting thing here is that vertically opposite angles are equal:

a° = b° c° = d°(in fact they are congruent angles)

AESTHETIC EDUCATION10TH GRADE: Q1P2Materials: A4 white cardboard, 2h pencil, compass, ruler, set squares.

PERPENDICULARS

Lines that are at right angles (90°) to each other.

1. Perpendicular passing through the middle of the segment AB.

a) Draw the segment AB

b) With the compass center at A and with a larger opening than half of the segment AB draw two arcs, above and below the segment AB.

c) With the same opening on the compass center at B, cut the previous arcs to obtain the points 1 and 2

d) Join the points 1 and 2, and we find the perpendicular.

NOTE: This procedure is also called perpendicular bisector

Definition: A line which cuts a line segment into two equal parts at 90°.

2. Perpendicular passing through a point c, on the AB segment

a) Draw the segment AB. Place the point C on the segment AB.

b) With the compass make center in C and with any opening cut with two arcs the segment AB and we place points 1 and 2.

c) Center in point 1, with an opening greater that the distance between 1 and 2, draw an arc above the segment AB

d) With the same opening repeat the same process now from point 2 and cut the previous arc and locate point 3.

e) Connect with a straight line the point C and 3, and find the perpendicular.

3. Perpendicular passing through a point C, outside the AB segment.

a) Draw AB segment and place the C point anywhere outside the AB segment.

b) Center at C, draw an arc that cut the AB segment.

c) Mark point 1 and 2 at the intersections of AB segment and the arc drawn.

d) Center at 1, and with any opening draw an arc below AB segment. Repeat from point 2 and mark point 3 at the crossing of the arcs.

e) Draw a line from C to point 3.

4. Perpendicular passing at the endpoint of AB segment.

a) Draw AB segment

b) Center at B, draw a semicircumference that cross AB, mark point 1.

c) With the same opening center at 1, and cut the semicircumference, mark 2, then repeat from 2 and find point 3.

d) With the same opening and center at 2, draw and arc above the semicircumference, repeat from 3 and cross the two arcs, mark point 4.

e) Draw a line from B to point 4.

5. Perpendicular passing at the endpoint of AB segment using a C point outside the segment.

a) Draw AB segment, place the point C anywhere outside AB near the endpoint of the segment.

b) Center at C and draw a semicircumference that pass through B, mark point 1.

c) Draw a line from 1 to C and extend until it cut the semicircumference, mark point 2

d) Draw a line from B to point 2

AESTHETIC EDUCATION10TH GRADE: Q1P2Materials: A4 white cardboard, 2h pencil, compass, ruler, set squares.

PARALLELS

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

Always the same distance apart and never touching.

1. Parallel passing through a point c, outside the AB segment.

a) Draw AB segment and place point C anywhere outside AB.

b) Center at C and draw a large arc which cuts AB segment, place point 1.

c) With the same opening center at 1 and draw a large arc that cut AB and pass through C, place point 2.

d) Center at 2 and set the width of the compass to the distance from 2 to C.

e) Center at 1 and draw an arc that cut the large arc, mark point 3.

f) Draw a line from 3 to C.

2. Parallel from a C point place on the AB segment.

a) Draw AB segment and place point C.

b) Center at C and with any opening draw a semicircumference that cut AB, place point 1 & 2.

c) Center at 1 and with an opening from 1 to 2 draw an arc, then repeat from 2 and cut the arc, place point 3 and 4.

d) Draw a line from 3 to 4 and extend.

3. Parallel from AB segment with a known X distance and 2 points on it.

a) Draw AB segment and place point 1 and 2 on the segment.

b) Draw a line segment with X distance of 2.8 cm

c) Set the width of the compass to the X distance, place the metal point on one end and the graphite on the other end of the X segment.

d) Center at 1 and draw an arc above AB segment, repeat from point 2.

e) Draw a line that pass on top the two arcs drawn.

4. Parallel from a given line that pass through a given point.

a) Draw AB segment, place point C on the segment and a point D outside it.

b) Draw a line from C to D and extend it.

c) Center at C and with any opening draw an arc which cuts AB segment and the given line CD, mark point 1 and 2.

d) Retain the width of the compass, center at D and draw an arc a similar arc that cut CD, place point 3.

e) Set the width of the compass to the distance from 1 to 2.

f) Center at 3 and draw an arc that cut the previously drawn arc, place point 4.

g) Draw a long line that passes by points D and 4.

AESTHETIC EDUCATION10TH GRADE: Q1P3Materials: A4 white cardboard, 2h pencil, compass, ruler, set squares.

REGULAR POLYGON

A 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.

(Not all polygons have those properties, but triangles and regular polygons do).

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

Regular Dodecagon12 sidesInterior angle 150 º

For you to know:

POLYGON NAMESgenerally accepted names

Sides Namen N-gon3 Triangle4 Quadrilateral5 Pentagon6 Hexagon

7 Heptagon8 Octagon10 Decagon12 DodecagonNames 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.

CONSTRUCTION OF REGULAR POLYGONS

CONSTRUCTION OF A PENTAGON

You will need a ruler and a compass.

First draw the horizontal and vertical lines.

For that, you first have to draw a horizontal line, name the line 1 and 2 respectively on both end points.

Step 1

Draw a horizontal line of 8cm, name both endpoints 1 and 2 respectively.

Obtain the perpendicular that passes through the midpoint, place point O (center).

Center at O (center) and draw a circumference with an opening from o to 2 (4 cm).

Place point A.

Step 2

Need to find the midpoint of the line segment that goes from the point O to 2.

Center at 2 and with an opening from 2 to O, draw to small arcs that cut the circumference.

Place points 3 and 4, draw a dashed line from those two points, and place point P.

Step 3

Using point P as a center, and with an opening from P to A draw an arc that cuts the horizontal line. Place point 5.

Step 4

Using point A as a center, and with an opening from A to 5 draw an arc that cuts the circumference. Place point B.

Step5

With the same opening center at B, and cut the circumference place point C. Holding the opening, repeat the procedure until you have D and E.

Step 6

Join the points ABCDE to construct the pentagon, use a fineliner (0.8mm) to draw each line.

How to build a five points star:

Using the same points ABCDE join in a different order, First a line from A to C, then from C to E, then E to B, then B to D, finally from D to A.

CONSTRUCTION OF A HEXAGON

You will need a ruler and a compass.

Step 1

Draw a horizontal line of 8cm, name both endpoints 1 and 2 respectively.

Obtain the perpendicular that passes through the midpoint, place point O (center).

Center at O (center) and draw a circumference with an opening from o to 2 (4 cm).

Place point A and point D.

Step 2

Center at A and with an opening from A to O cut the circumference in two places, mark point B and point F.

Then center at D and with an opening D to O cut the circumference in two parts, mark point C and point E.

Finally join points ABCDEF to construct the Hexagon.

How to build a six points star:

Using the same six points of the Hexagon construction, join them in order to build to triangles. First is triangle ACE, the second one is BDF.

CONSTRUCTION OF A HEPTAGON

You will need a ruler and a compass.

Step 1

Draw a vertical line A1 of 8cm, mark at the center of that line the point O.

Using the compass, center at 1, and with an opening from 1 to O, draw an arc that cut the circumference, place point 2 and 3.

Place point P on the intersection.

Step 2

With the compass, first set the opening equal to the distance between P and 2 (see the figure 2), and using that opening center at A and cut the circumference place point B.

Holding the opening repeat until you get points C, D, E, F, G.

Step 3

Join the seven points to draw the heptagon.

How to build a seven points star:

Join the points in the next order:

1) A to C 2) C to E 3) E to G 4) G to B

4) B to D 5) D to F 6) F to A. Then erase the internal dashed lines, and use fineliner (0.8).

CONSTRUCTION OF AN OCTAGON

Steps.

1. Draw line segment CG = 8cm.2. Find the perpendicular bisector for CG, place

point O.3. Center at O and draw a circumference with

an opening from O to G (4 cm).4. Place point A and E where the circumference

and the perpendicular bisector intersect.5. With the compass, center at G and with an

opening from G to O, draw an arc, holding the opening, center at A and cut the recently drawn arc, place point 3.

6. Draw a line from 3 to O and extend (the line have to cut the circumference) Place point H and D.

7. With the compass, center at C and with an opening from C to O, draw an arc, holding the opening, center at A and cut the recently drawn arc, place point 4.

8. Draw a line from 4 to O and extend (the line have to cut the circumference) Place point B and F.

9. Join the points in order. ABCDEFGHA to build the Octagon.

How to build an eight points star:

Join the points in the next order:

1) A to D 2) D to G 3) G to B 4) B to E

4) E to H 5) H to C 6) C to F 4) F to A

Note: You have to skip to points each time.

You can draw lines like the ones you see below (dashed lines) in order to make a design.

An eight points star with design.

Note: the use of different colors.

CONSTRUCTION OF A NONAGON

Steps.

1. Draw a line segment of 8cm, place point 1 and 2 on the endpoints.

2. Draw the perpendicular bisector (center at 1 with an opening from 1 to 2 draw an arc above and below, repeat from 2), place point O.

3. Draw a circumference from O, with and opening from 1 to O. (r = 4cm). Place point A and 5.

4. With the compass, center at A and with an opening from A to O draw and arc that cuts the circumference. Place point 6.

5. First extend the horizontal line, then center at 5, and with an opening from 5 to 6 draw an arc that cuts the extended horizontal line. Place point 7.

6. Center at 7 and with an opening from 7 to A, draw an arc that cuts the horizontal line segment. Place point 8.

7. The x distance, from 1 to 8 will be the distance of the side for the nonagon. Set the compass opening to match the distance from 1 to 8.

8. Center at A and cut the circumference, place point B, then repeat from B to place C and

continue repeating the process until you have all the points needed.

9. Join the points in the correct order to build the nonagon.

How to build an eight points star:

There are different ways to join the points and each one will build a different star.

In the example below you will notice that the star is built by joining the points by skipping one point each time.

The lines that will form the star.

The star finished.