Exploring Angles: Definition, Classification, and Properties

1. Geometry Exploring Angles Section 1-6

2. In this section we will discuss the definition and parts of an angle as well as how an angle divides up a plane. We will learn to identify angles and to classify those angles as acute, right, straight, or obtuse angles. We will learn to use the Angle Addition Postulate to find the measure of angles. We will determine and use angle congruence and and the bisector of an angle. …\GeoSec01_06.ptt

3.  ray - PQ is a ray. if it is the set of points consisting of PQand all points Sfor which Q is betweenP and S. It is a half line. • P • Q • S Note how a ray is symbolized. In the symbol, the arrow always points to the right and the first letter on the left is the endpoint of the ray. No matter the orientation, the ray PQ is always symbolized the same.  • S • Q • S • Q • P • P …\GeoSec01_06.ptt

4. This is a line. • J • L For connivance, we could select point Jon the left of K and point Lto the right of K. This permits us to name the two rays, KJ and KL.     Rays KJ and KL. Are called opposite rays. Opposite rays have a common endpoint and they are collinear. • K Select any point, say K, anywhere on the line. Point K will divide the line into two equal rays. The ray to the left of K is a half line and the ray to the right of K is a half line. …\GeoSec01_06.ptt

5. side side An angle is a figure formed by two noncollinear rays with a common endpoint. vertex An angle can be designated several ways. …\GeoSec01_06.ptt

6. The angle symbol A number located in the interior of the angle. 1  1 …\GeoSec01_06.ptt

7. A • B • • C The vertex is in the middle of the angle designation. Or using points on the angle itself.  ABC or  CBA Both the same angle …\GeoSec01_06.ptt

8. W • • Z interior X • • Y An angle separates a plane into three parts. The angle, the interior, and the exterior. exterior If a point is NOT in the interior and it is NOT on the angle itself, then it is exterior to the angle.. …\GeoSec01_06.ptt

9.  Postulate 1-3, Protractor Postulate - Given ABand a number r between 0 and 180, there is exactly one ray with endpoint A, extending on each side of AB, such that the measure of the angle formed is r.  This states that there is one and only one specific angle, say 30o, on either side of a ray. B • 30o A • 30o …\GeoSec01_06.ptt

10. P • R • • Q • S Postulate 1-4, Angle Addition Postulate - If Ris in the interior of PQS, thenmPQR + mRQS= mPQS. IfmPQR+ mRQS= mPQS, thenRis in the interior of PQS This postulate states that the sum of two angles, mPQR and mRQS that are interior to the angle is mPQS. …\GeoSec01_06.ptt

11. Definition of Right, Acute, Obtuse, Straight Angles - •  Ais a right angle ifm Ais90. •  Ais an acute angle ifm Ais less than90. • Ais an obtuse angle ifm Ais greater than90and less than 180. • Ais a straight angle ifit is formed by two opposite rays. It measures180. Congruent Angles are angles that have the same measure and angles with the same measure are congruent. Ifm A =m B, then A  B AND If  A  B, thenm A = m B …\GeoSec01_06.ptt

12. • A • C  1 2 BDbisectsABC, therefore 1  2 • B Segment bisector divides a segment into two equal pieces. An angle bisector divides an angle into two equal angles, which are congruent.. • D …\GeoSec01_06.ptt

13. In this section we will discuss the definition and parts of an angle as well as how an angle divides up a plane. We will learn to identify angles and to classify those angles as acute, right, straight, or obtuse angles. We will learn to use the Angle Addition Postulate to find the measure of angles. We will determine and use angle congruence and and the bisector of an angle. …\GeoSec01_06.ptt

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