1) The document defines an angle as being formed by two rays with a common endpoint called the vertex. Angles can have points in their interior, exterior, or on the angle. 2) There are three main ways to name an angle: using three points with the vertex in the middle, using just the vertex point when it is the only angle with that vertex, or using a number within the angle. 3) There are four types of angles: acute, right, obtuse, and straight. Angles are measured in degrees with a full circle being 360 degrees.

1. Lesson 1-4 Angles Lesson 1-4: Angles

3. Naming an angle: (1) Using 3 points (2) Using 1 point (3) Using a number – next slide Lesson 1-4: Angles 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

4. Naming an Angle - continued Lesson 1-4: Angles 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 B C

6. 4 Types of Angles Lesson 1-4: 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  .

9. Angle Addition Postulate Lesson 1-4: Angles The sum of the two smaller angles will always equal the measure of the larger angle . Complete: m  ____ + m  ____ = m  _____ MRK KRW MRW Postulate:

10. Example: Angle Addition Lesson 1-4: Angles 3x + x + 6 = 90 4x + 6 = 90 – 6 = –6 4x = 84 x = 21 K is interior to  MRW, m  MRK = (3x)  , m  KRW = (x + 6)  and m  MRW = 90 º. Find m  MRK. 3x x+6 Are we done? m  MRK = 3x = 3 • 21 = 63 º First, draw it!

12. Congruent Angles Lesson 1-4: Angles  3   5. 5 3 Definition: If two angles have the same measure, then they are congruent. Congruent angles are marked with the same number of “arcs”. The symbol for congruence is  Example: