- False.
- True. , but the absolutevaluesign makesthemboth positive.
- Number8 is false.See the diagrambelowfor a counterexample.To make8 true,we needto add
somethinglike: “If points , , and are collinear, and is between and , then if
and , then .”
Raysand Angles
LearningObjectives
- Understandand identifyrays.
- Understandand classifyangles.
- Understandand applythe protractorpostulate.
- Understandand applythe angleadditionpostulate.
Introduction
Now that you knowaboutline segmentsand how to measurethem,you can applywhatyou havelearned
to othergeometricfigures.This lessondealswith rays and angles,and you can applymuchof whatyou
havealreadylearned.We will try to help you see the connectionsbetweenthe topicsyou studyin this book
insteadof dealingwith themin isolation.This will give you a morewell-roundedunderstandingof geometry
and makeyou a betterproblemsolver.
Rays
A ray is a part of a line with exactlyone endpointthat extendsinfinitelyin one direction.Raysare namedby
their endpointand a pointon the ray.
The ray aboveis called. The first letterin the ray’s nameis alwaysthe endpointof the ray, it doesn’t
matterwhichdirectionthe ray points.
Rayscan representa numberof differentobjectsin the real world.For example,the beamof light extending
from a flashlightthat continuesforeverin one directionis a ray. The flashlightwouldbe the endpointof the
ray, and the light continuesas far as you can imagineso it is the infinitelylong part of the ray. Are there
otherreal-lifeobjectsthat can be representedas rays?
Example 1