3. Angle. Two straight lines which meet at a point form an angle. The two lines are called the sides of the angle. The point of meeting is called the vertex of the angle.

This angle is read, "the angle HKE," "the angle EKH," or "the angle K." When

all three letters are read, the letter at the vertex is read between the other two.

The lines KH and KE are the sides of the angle and the point K is the vertex of the angle.

B

An angle may also be designated by a letter placed within the angle near the vertex. In this figure, the angle BDA may be read, "the angle y," and the angle ADE may be read, "the D angle z." The angle BDE may also be read, “the angle D."

E

4. Protractor. An instrument for determining the number of degrees in an angle, and also for drawing an angle of a given number of degrees is called a protractor.

5. Measuring an Angle. To measure an angle, place the point B of the protractor on the vertex of the angle. Make one edge of the protractor, as BD, coincide with one side of the angle, as BA. The position of the other side BC indicates the number of degrees in the angle. The angle ABC is an angle of 50°.

Measure each of the following angles with the protractor.

6. Drawing an Angle. To draw an angle, first draw a straight line, which is to be one side of the angle, as BC in the figure, § 4. If the angle is to be 50°, place the protractor so that the side BC falls along the 50° mark, then draw the side BA along the edge. The angle ABC is the required angle of 50°. Care should be taken to draw all angles accurately.

Draw angles of 20°, 45°, 75°, 90°, 125°, 135°, 180°, 35°, 145°, 110°.

7. Accuracy in Drawing Lines and Angles. In drawing a line through a point, first place the pencil upon the point, then bring the ruler up to the pencil. In drawing a line through two points, try the pencil at each point, moving the ruler until the line passes exactly through both points. In drawing an angle with the vertex at a given point, care should be taken to make the sides meet at that point.

3. Angle. Two straight lines which meet at a point form an angle. The two lines are called the sides of the angle. The point of meeting is called the vertex of the angle.

This angle is read, "the angle HKE,"

"the angle EKH," or "the angle K." When

all three letters are read, the letter at the vertex is read between the other two.

The lines KH and KE are the sides of the angle and the point K is the vertex of the angle.

An angle may also be designated by a letter placed within the angle near the vertex.

In

B

E

this figure, the angle BDA may be read, "the angle y," and the angle ADE may be read, "the D angle z." The angle BDE may also be read, "the angle D."

4. Protractor. An instrument for determining the number of degrees in an angle, and also for drawing an angle of a given number of degrees is called a protractor.

5. Measuring an Angle. To measure an angle, place the point B of the protractor on the vertex of the angle. Make one edge of the protractor, as BD, coincide with one side of the angle, as BA. The position of the other side BC indicates the number of degrees in the angle. The angle ABC is an angle of 50°.

Measure each of the following angles with the protractor.

6. Drawing an Angle. To draw an angle, first draw a straight line, which is to be one side of the angle, as BC in the figure, § 4. If the angle is to be 50°, place the protractor so that the side BC falls along the 50° mark, then draw the side BA along the edge. The angle ABC is the required angle of 50°. Care should be taken to draw all angles accurately.

Draw angles of 20°, 45°, 75°, 90°, 125°, 135°, 180°, 35°, 145°, 110°.

7. Accuracy in Drawing Lines and Angles. In drawing a line through a point, first place the pencil upon the point, then bring the ruler up to the pencil. In drawing a line through two points, try the pencil at each point, moving the ruler until the line passes exactly through both points. In drawing an angle with the vertex at a given point, care should be taken to make the sides meet at that point.

8. Bisector. A figure is bisected when

it is divided into two equal parts.

B

A

The line AC is bisected by the point B, since it is divided into the two equal parts, AB and BC. The point B is the bisector of the line AC.

The line KE is the bisector of the angle

K, since it divides the angle into the two equal angles, x and z.

H

E

-M

With the protractor, draw angles of 120°, 150°, 30°, 70°, 170°, and 80°. Bisect these angles with the protractor.

9. Compasses. A pair of compasses is an instrument for constructing circles and laying off lengths on lines. The compasses can be adjusted for any desired distance between the two points A and B.

10. Circle. Place one point A of the compasses on a point

A B

O, and adjust the compasses until the other
point B falls on point D. Keeping the point at
O stationary, move point B around point O
until it returns to point D. The distance be- D
tween the points A and B remains unchanged
as point B moves about point 0.

E

C

The line DEF is a curved line called a circle. The point 0 is the center of the circle.

A straight line drawn from the center to any point on the circle is a radius.

Thus the line OE is a radius of the circle. The lines OE and OF are radii of the circle.

Any portion of a circle is an arc.

H

Thus HK is an arc. In the circle whose center is 0,

FCE and FDE are arcs.

Construct ten circles, using a different radius for each.