# UNIT 04: TRIANGLES

## 1. ISOSCELES TRIANGLE

Draw an isosceles Triangle known one of its equal sides b = 4 cm. and one of its equal angles A = 30°.

## 2. ISOSCELES TRIANGLE

Draw an isosceles Triangle known the unequal side c = 5 cm. and the unequal angle C = 45°.

## 3. RIGHT TRIANGLE

Draw a right triangle known its legs b = 5 cm. and c = 4 cm.

## 4. SCALENE TRIANGLE

Draw an scalene triangle known side a = 6 cm., side b = 5 cm. and the angle between them C = 40°.

## 5. SCALENE TRIANGLE

Draw a triangle known its side a = 5 cm., its angle A = 60° and other of its angles C = 45°.

## 6. SCALENE TRIANGLES

Draw the triangles whose sides measure c = 5 cm. and b = 6 cm. and one of their angles is A = 45°.

Here you can download and print the photocopy that I gave you on Monday to continue practising the construction of triangles. Nex week I will share the solutions!

# UNIT 04: TRIANGLES

## 1. EQUILATERAL TRIANGLE (l = 5 cm.)

STEPS:

1. Draw the given side and call its endpoints A and B.
2. Center your compass in point A and open it to point B, draw an arc.
3. Now center the compass in point B and with the same measure, draw another arc.
4. Where these two arcs intersect each other, we will get point C.
5. Join point A with point C and do the same with point B so you get the equilateral triangle ABC.

## 2. ISOSCELES TRIANGLE (a = b = 4.5 cm., c = 3.5 cm.)

STEPS:

1. Draw the different side, in our case side c whose measure is 3.5 cm.
2. Take the measure of the other two sides with your compass, in our case 4.5 cm.
3. With this measure draw an arc centering your compass in point A.
4. With the same measure draw another arc centering your compass in point B.
5. Where these two arcs intersect each other, we will get point C.
6. Join point A with point C and do the same with point B so you get the isosceles triangle ABC.

## 3. SCALENE TRIANGLE (a = 7 cm., b = 4.5 cm., c = 5.5 cm.)

STEPS:

1. Draw a side, for example side a = 7 cm.
2. Measure another side with your compass, for example b = 4.5 cm.
3. With this measure, draw an arc centering your compass in point C.
4. Measure the last side with your compass, c = 5.5 cm.
5. With this measure draw an arc centering your compass in point B.
6. Where these two arcs intersect each other, we will get point A.
7. Join point A with point C and do the same with point B so you get the scalene triangle ABC.

## 4. TRIANGLES (a = 6 cm., b = 4 cm., B = 30º)

In this exercise we can get two possible solutions.

STEPS:

1. Draw the given side a and call its endpoints B and C.
2. Draw a 30º angle whose vertex is point B, to do this you have to follow the steps given to draw the trisection of an angle.
3. Measure side b with your compass, in our case b = 4 cm.
4. Center your compass in point C and draw an arc. Where this arc interects the side of the 30º angle we will get points A1 and A2.
5. Bear in mind that in this exercise we can get two possible solutions A1BC and A2 BC.

## 5. RIGHT TRIANGLE (a = 6 (Hypotenuse), b = 3 cm.)

STEPS:
As we have to draw a right triangle we have to remember that this triangle has a 90º angle and that this angle faces the hypotenuse.

1. Draw the given side b (3 cm.) and call its endpoints A and C.
2. Draw a 90º angle whose vertex is point A, to do this you will need to follow the steps given to draw the perpendicular to a ray.
3. Measure the hypotenuse with your compass, in our case 6 cm.
4. Center your compass in point C, and where this arc intersects the right angle we will get point B, the last vertex of our triangle.

## 6. TRIANGLE (a = 6.5 cm., B = 30º, C = 105º)

STEPS:

1. Draw the given side a and call its endpoints B and C.
2. Draw a 30º angle whose vertex is point B, to do this you have to follow the steps given to draw the trisection of an angle.
3. Draw a 105º angle whose vertex is point C, to do this you have to follow the steps given to draw a 105º angle.
4. Where these two lines intersect you will get vertex A.

Here you can see the solution of the complete drawing sheet:

# HANDLING THE SET SQUARE

### How should we handle the set square?

You have to handle your set square softly and with accuracy without exercising too much pressure on them, only the needed one to avoid movement.
To draw parallel lines to one direction we have to follow these steps:

1. The 45 set square hypotenuse (longest side) is placed attached to the line to which we want to draw the parallels.
2. The 60-30 set square hypotenuse is attached to the 45 set square leg.
3. Fix the 60-30 set square and move the 45 set square upwards or downwards drawing the desired parallel lines along its hypotenuse.

If we want to draw perpendicular lines to one direction, we will have to follow the first two steps as stated for parallel lines and then the following ones:

1. Having fixed the 60-30 set square, the 45 set square is turned until the other leg is attached to the hypotenuse of the 60-30 set square.
2. Draw the perpendicular line along the hypotenuse of the 45 set square.

# UNIT 01: BASIC ELEMENTS OF PLASTIC EXPRESSION

## EXERCISE 02: PARALLEL LINES

### How do we use the set square?

You have to handle your set square softly and with accuracy without exercising too much pressure on them, only the needed one to avoid movement.
To draw parallel lines to one direction we have to follow these steps:

1. The 45 set square hypotenuse (longest side) is placed attached to the line to which we want to draw the parallels.
2. The 60-30 set square hypotenuse is attached to the 45 set square leg.
3. Fix the 60-30 set square and move the 45 set square upwards or downwards drawing the desired parallel lines along its hypotenuse.

If we want to draw perpendicular lines to one direction, we will have to follow the first two steps as stated for parallel lines and then the following ones:

1. Having fixed the 60-30 set square, the 45 set square is turned until the other leg is attached to the hypotenuse of the 60-30 set square.
2. Draw the perpendicular line along the hypotenuse of the 45 set square.