- Eachanglewill measure If two anglesare complementary, then the sum of their measuresis
Sincethe anglesare congruent,they musthavethe samemeasure, [Diff: 3].
- [Diff: 2]
- This is similar to number 10. The two angles form a linear pair so they are supplementary.
. Sincewe know , we can concludethat eachangle
measures [Diff: 3].
PerpendicularTransversals
LearningObjectives
- Identifythe implicationsof perpendiculartransversalson parallellines.
- Identifythe conversetheoremsinvolvingperpendiculartransversalsand parallellines.
- Understandand use the distancebetweenparallellines.
Introduction
In the last lesson,you learnedaboutperpendicularintersections.You knowthat whentwo lines are perpen-
dicularthey form four right angles.This lessoncombinesyour knowledgeof perpendicularlines with
your knowledgeof parallellines and transversals.
PerpendicularTransversalsand Parallellines
Whentwo linesare cut by a transversal,a numberof specialanglesare formed.In previouslessons,you
learnedto identifycorrespondingangles,alternateinteriorangles,alternateexteriorangles,and consecutive
interiorangles.You learnedthat the lines crossedby the transversalare parallelif and only if corresponding
anglesare congruent.Likewisealternateinteriorand alternateexterioranglesare congruentand interior
angleson the sameside of the transversalare supplementaryif the linescrossedby the transversalare
parallel.Whenthe transversalis perpendicular, somethinginterestinghappenswith theseangles.Observe
the anglemeasuresin the examplebelow.
Example 1
Lines and are paralleland