Jose M Bravo Jr. Jose M Bravo Jr.

Chapter 11.1Chapter 11.1Introduction to Basic GeometryIntroduction to Basic Geometry

Basic Geometric ConceptsBasic Geometric Concepts

Point, Line, Line SegmentPoint, Line, Line Segment

DefinitionsDefinitionsA A pointpoint is an exact location in space. A point has no dimensions.is an exact location in space. A point has no dimensions.

AA lineline is a collection of points along a straight path that extends endlessly in both is a collection of points along a straight path that extends endlessly in both directions.directions.

A A line segmentline segment is a part of a line having two endpoints. A line segment has only is a part of a line having two endpoints. A line segment has only one dimension-its length. (Example AB on the figure above.)one dimension-its length. (Example AB on the figure above.)

A B

Ray, Angle, and PlaneRay, Angle, and PlaneA rayA ray is a part of a line having only one endpoint. is a part of a line having only one endpoint.

An angleAn angle consists of two rays that have a common consists of two rays that have a common endpoint called the vertex of the angle.endpoint called the vertex of the angle.

A planeA plane is a flat surface that extends endlessly in all is a flat surface that extends endlessly in all directions.directions.

BA

CVertex

DefinitionsDefinitionsA straight angle is 180A straight angle is 180

ExampleExample

A right is an angle A right is an angle That measures 90That measures 90

An acute angle is less than 90An acute angle is less than 90

An obtuse angle is more than An obtuse angle is more than 90 and less than 18090 and less than 180

Angles are measured in Angles are measured in degrees ( )degrees ( )

Angles are classified according Angles are classified according to their measures.to their measures.

BA C

EF

D

YZ

X

D

E

C

Complementary and Complementary and Supplementary AnglesSupplementary Angles

Complementary angles are two angles whose Complementary angles are two angles whose sum is 90.sum is 90.

A

25

B65

Supplementary angles are two angles whose sum is 180

C40

D

140

Intersecting lines, Parallel lines, Intersecting lines, Parallel lines, Perpendicular linesPerpendicular lines

Intersecting lines are two lines that meet.Intersecting lines are two lines that meet.

Parallel lines are two lines in the same plane that do not intersect.

Perpendicular lines are two lines that intersect to form right angles.

BADD C

E

E F

G H

Symbol for right angle

QT

SR

P

Vertical AnglesVertical AnglesVertical anglesVertical angles are two equal angles formed are two equal angles formed by two intersecting lines.by two intersecting lines.

120A

6060120

EC

DB