# ANGLES

In geometry, an **angle** is the figure formed by two rays, called the **sides** of the angle, sharing a common endpoint, called the **vertex** of the angle.

## TYPES OF ANGLES

- Angles equal to
**90º**are called a**RIGHT ANGLES**. Two lines that form a right angle are said to be perpendicular. - Angles equal to
**180º**are called**STRAIGHT ANGLES**. - Angles equal to
**360º**are called**ROUND OR FULL ANGLES**. - Angles smaller than a right angle (less than 90°) are called
**ACUTE ANGLES**. - Angles larger than a right angle and smaller than a straight angle (between 90° and 180°) are called
**OBTUSE ANGLES**.

## 1. TRANSLATION OF AN ANGLE

In Geometry, “Translation” simply means **moving**…without rotating, resizing or anything else,just moving.

If we want to draw an angle equal to a given one with vertex at a given point V.

STEPS:

- Center the compass at vertex of the given angle and draw an arc intersecting both sides of it. Without changing the radius of the compass, center it at point V and draw another arc
- Set the compass radius to the distance between the two intersection points of the first arc.
- Now center the compass at the point where the second arc intersects ray V.
- Mark the arc intersection point 1.
- Join point V with point 1 so you get the equal angle.

## 2. ANGLE BISECTOR

It is a line which divides the angle in two equal parts. Each point of an angle bisector is equidistant from the sides of the angle.

STEPS:

- Draw an angle.
- Center the compass at vertex of the given angle and draw an arc intersecting both sides of it. We get 1 and 2
- Center the compass at point 1 and draw an arc.
- With the same measure center it at point 2 and draw another arc.
- Where these arcs cross we get point 3.
- If we join point 3 with the vertex of the angle we get the angle bisector.

## 3. TRISECTION OF AN ANGLE – DIVIDE A RIGHT ANGLE IN THREE EQUAL PARTS

STEPS:

- Draw a right angle angle, to do this we use the steps of the perpendicular to a ray
- Center the compass at vertex of the right angle (V) and draw an arc intersecting both sides of it. We get 1 and 2.
- Without changing the radious of the compass center the compass at point 1 and draw an arc, so we get point 3.
- Without changing the radious of the compass center the compass at point 2 and draw an arc, so we get point 4.
- If we join points 3 and 4 with the vertex of the angle we get the three equal parts of the right angle.

## 4. 45º ANGLE

STEPS:

- Draw a right angle angle, to do this we use the steps of the perpendicular to a ray
- Draw the angle bisector of the right angle that you have drawn

## 5. ADDITION OF ANGLES

The addition of two angles is another angle whose measure is the addition of the measures of those two angles.

STEPS:

- Copy angle A using translation of an angle.
- From this new angle copy angle B.
- The solution is angle C.

## 6. SUBTRACTION OF ANGLES

The subtraction of two angles is another angle whose measure is the subtraction of the measures of those two angles.

STEPS:

- Copy angle B (the biggest one) using translation of an angle.
- From this new angle copy angle A.
- The solution is angle C.

## SOLUTION OF DRAWING SHEET

Here you can see how to compose the complete drawing sheet, remember that you must underline the blue lines with your 0.4 technical pen, the red ones with 0.8 and the black ones with 0.2.

Here you can see one of our students’ drawing sheets:

ANGLES – DRAWING SHEET NUMBER 6 – EXAMPLE 2013