1.4+Angles

(Found in text pages 26-32) **
 * Lesson 1.4 Angles

In this section you will learn all about classifying, naming, measuring, and calculating measures of angles. You will also learn how to use two of the angle postulates- The Protractor Postulates, and the Angle Addition Postulates.

The goals of this section are how to learn how to: - Apply the angle addition postulate, and the Protractor Postulate. - Classify angles are right, acute, obtuse, straight, and adjacent. - And be able to identify congruent angles.

Here are two helpful webpages that will help teach this topic further than what I've already taught: http://www.homeschoolmath.net/teaching/g/angles.php http://www.cliffsnotes.com/study_guide/Angles-and-Angle-Pairs.topicArticleId-18851,articleId-18772.html

__Acute Angle__-** Any angle that measures ANYTHING LESS THAN 90 degrees. **__**Congruent Angles-**__ ** Angles that have the same measure ** __**Interior Of An Angle-**__ ** All points that are between the points that lie on each side of the angle. ** __**Exterior Of An Angle-**__ ** All points that are not on the angle or in it's interior. ** __**Adjacent Angles-**__ Two angles are adjacent angles if they have a common vertex and side, but have no common interior points.
 * Vocabulary Definitions:**
 * __Angle-__ A shape that consists of two different rays that have the same initial point. The rays are called the sides of the angle.
 * __Obtuse Angle-__** Any angle that measures ANYTHING MORE THAN 90 degrees.
 * __Right Angle-__** Any angle that measures 90 degrees exactly.
 * __Straight Angle-__** Basically a straight line and it MUST measure 180 degrees exactly.
 * __Vertex Of An Angle-__ The initial point of the angle.

An **angle** consists of two different rays that have the same initial point. The rays are the **sides** of the angle. The initial point is the **vertex** of the angle.

The angle that has sides and  is denoted by //BAC//, //CAB//, or //A//. The point //A// is the vertex of the angle.

Protactor Postulate:
 * Postulates:

Consider a point A on one side of segment OB. The rays of the form OA can be matched one to one with the real numbers from 0 to 180 degrees. The measure of angle AOB is equal to the absolute value of the difference between the real numbers for ray OA and ray OB.

Angle Addition Postulate: If P is in the interior of angle RST then, the measure of angle RSP + the measure of angle PST = the measure of angle RST. **

 A point is in the interior of an angle if it is between points that lie on each side of the angle. A point is in the exterior of an angle if it is not on the angle or in its interior. **(In the example shown above, point D is in the interior, and point E is in the exterior)
 * Interior & Exterior- When Is A Point on The Exterior or Interior of the Angle? [[image:mcd_ma_geo_lsn_0395937779_p26_f08.gif]]


 * Sample Problems: **

http://www.math.com/school/subject3/practice/S3U1L4/S3U1L4Pract.html** http://www.brainpop.com/math/geometryandmeasurement/angles/quiz/ http://www.explorelearning.com/index.cfm?method=cResource.dspView&ResourceID=282
 * Online Practice Problems: