Chapter 10: Geometry Section 10.1: Visualization

Important Objects ObjectVisualizationCharacteristics PointA tiny dotHas no size or shape LineAn infinitely long stretched string with no beginning or end Has no thickness PlaneAn infinite flat piece of paper with no beginning or end Has no thickness Line segment: part of a line lying between two points, called the endpoints of that segment Ray: part of a line lying on one side of a point

Where objects lie In the plane: on an infinite 2-dimensional surface In space: in an infinite 3-dimensional room

Section 10.2: Angles Def: (a) An angle is the amount of rotation about a fixed point (b) An angle is the region between two rays with a common endpoint Def: Two angles are congruent if they both represent the same amount of rotation

Measuring Angles Def: Angles are measured in degrees, where a full circle rotation is considered to be 360˚. Def’s: acute angle: < 90˚ right angle: = 90˚ obtuse angle: > 90˚ straight angle: = 180˚

Angles formed by two lines Theorem 1: When two lines meet in a plane, they form four angles, which sum to 360˚. Def: If the angles formed by two intersecting lines are all 90˚, then the two lines are perpendicular. Def: If two lines never meet, they are parallel.

Configurations of 3 lines in a plane

Theorem 2: The three angles in a triangle sum to 180˚.