Angles and pairs of angganon arte kaoales.pptx

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1. Angles and pairs of angles Math fundamentals, angle pairs, and polygons

2. Angles and angle Measures Definition An angle is formed by two noncollinear rays that have a common endpoint. The endpoint is the vertex of the angle, and each ray is the side of the angle

3. Classification of angles according Definition A n acute is an angle, which measure is less than 90 °. A right angle is angle, which measure is equal to 90°. It can also be defined as an angle which sides are perpendicular. . An obtuse angle is an angle, which measure is more than 90 °

4. Congruent angles Definition Two angles are congruent if they have same measure. . Means “angle P is congruent to Angle Q”. Similar markings are used to indicate congruent angles. Definition

5. Interior and Exterior of an angle. An angle in a plane separates the plane into three sets of points: the angle itself, the interior of the angle, and the exterior of the angle. The concept of interior is applied in the next definition.

6. Interior point of an angle. Definition A point is in the interior of an angle if it does not lie on the angle itself and lies on a segment which endpoints are on the sides of the angle.

7. Bisector of an Angle Definition If D is in the interior of Then is an angle bisector of Definition

8. Properties of angle pairs.

9. Complementary and Supplementary angles. TERMS ILLUSTRATIONS Two angles are supplementary if the sum of their measures is 180. Each angle is called a supplement of the other. If are supplementary angles, then m a+m b=180. Two angles are complementary if the sum of their measures is 90. Each angles is called a complement the other. If 1 and 2 are complementary angles, then m 1 + m 2=90 TERMS ILLUSTRATIONS Two angles are supplementary if the sum of their measures is 180. Each angle is called a supplement of the other. Two angles are complementary if the sum of their measures is 90. Each angles is called a complement the other.

10. Adjacent angles Definition Adjacent angles are two coplanar angles that have a common side between them but have no interior points in common.

11. Linear Pairs Definition If two angles are adjacent and supplementary, then they are called linear pair.

12. Vertical angles Definition Vertical angles are nonadjacent angles formed by two intersecting lines.

13. Angles at a point Definition All angles having the same vertex around a point are called angles at a point. The sum of the measures of angles at a a point 360 degrees