Introduction to Angles

Definitions Sides: The two rays that make up the angle. side A B C Vertex: Common endpoint of the two rays that make an angle. A B C

Lesson 1-4: Angles 3 Angle and Points An Angle is a figure formed by two rays with a common endpoint, called the vertex. vertex ray Angles can have points in the interior, in the exterior or on the angle. Points A, B and C are on the angle. D is in the interior and E is in the exterior. B is the vertex. A B C D E

Lesson 1-4: Angles 4 Naming an angle: (1) Using 3 points (2) Using 1 point (3) Using a number – next slide Using 3 points:vertex must be the middle letter This angle can be named as Using 1 point:using only vertex letter * Use this method is permitted when the vertex point is the vertex of one and only one angle. Since B is the vertex of only this angle, this can also be called. A B C

Lesson 1-4: Angles 5 Naming an Angle - continued Using a number:A number (without a degree symbol) may be used as the label or name of the angle. This number is placed in the interior of the angle near its vertex. The angle to the left can be named as. * The “1 letter” name is unacceptable when … more than one angle has the same vertex point. In this case, use the three letter name or a number if it is present. 2 A BC

Definitions Degrees: The unit of measure for angles. Indicates the amount of rotation. Measure of an angle: Smallest amount of rotation about the vertex from one ray to the other. Use a curved line to indicate the angle. A B C

Lesson 1-4: Angles 7 Example Therefore, there is NO in this diagram. There is K is the vertex of more than one angle.

Lesson 1-4: Angles 8 4 Types of Angles Acute Angle: an angle whose measure is less than 90 . Right Angle: an angle whose measure is exactly 90 . Obtuse Angle: an angle whose measure is between 90  and 180 . Straight Angle: an angle that is exactly 180 .

Definitions Congruent Angles: Angles that have the same degree measure. Used a curved line above an equal sign to indicate congruence. A B C X Y Z Said: “Angle ABC is congruent to angle XYZ.”

Practice X M G A PName all the angles in this figure.

Measuring, calculating and drawing angles...

A protractor Here is a standard protractor like you use in the classroom.

When we use a protractor, we need to line it up correctly. You need to make sure the protractor is lined up correctly. Is this ready to measure the angle?

Were you right it wasn’t Look for the upside down ‘T’ in the middle of the straight line on your protractor. This needs to be exactly on the vertex of your angle.

We need to remember..... It doesn’t matter which way round the angle is, you ALWAYS need to line the upside down ‘T’ to the vertex of the angle.

Now you are ready. Read from the 0°, and follow the inner set of numbers.

Once you reach 30° you need to be careful!!! You then need to look at the 1° markings on the outer set of numbers.

What does it measure? This angle measures 35°.