# UNIT 04: TRIANGLES

## EXERCISE 04: TRIANGLES

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

STEPS:

- Draw the given side and call its endpoints A and B.
- Center your compass in point A and open it to point B, draw an arc.
- Now center the compass in point B and with the same measure, draw another arc.
- Where these two arcs intersect each other, we will get point C.
- 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:

- Draw the different side, in our case side c whose measure is 3.5 cm.
- Take the measure of the other two sides with your compass, in our case 4.5 cm.
- With this measure draw an arc centering your compass in point A.
- With the same measure draw another arc centering your compass in point B.
- Where these two arcs intersect each other, we will get point C.
- 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:

- Draw a side, for example side a = 7 cm.
- Measure another side with your compass, for example b = 4.5 cm.
- With this measure, draw an arc centering your compass in point C.
- Measure the last side with your compass, c = 5.5 cm.
- With this measure draw an arc centering your compass in point B.
- Where these two arcs intersect each other, we will get point A.
- 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:

- Draw the given side a and call its endpoints B and C.
- 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.
- Measure side b with your compass, in our case b = 4 cm.
- 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.
- 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.

- Draw the given side b (3 cm.) and call its endpoints A and C.
- 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.
- Measure the hypotenuse with your compass, in our case 6 cm.
- 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:

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

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

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