Geometry-Definitions, Postulates,
Properties, & Theorems
CH 3-Perpendicular & Parallel Lines
Geometry I
Navigating the PowerPoint
 Takes you to the main menu
 Takes you to the help page
 There are other buttons explained throughout
the PowerPoint
Main Menu
Click the buttons to navigate to the different slides
(It’s best to follow the arrows)
✪
Background
Info
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Quiz Info
(next day)
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Theorems
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Quizlet
(HW)
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Quiz (end
of class)
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Theorems
Cont.
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Helppp!!
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Basic
Definitions
Postulates
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Background Info
 A theorem is a statement that has been proven on previously
established statements like other theorems and postulates.
 A theorem is a proof of the truth of the resulting expression.
 A theorem is a logical argument in the sense that if a hypothesis
is true then the conclusion must also be true.
 A postulate is a statement that is accepted without proof and is
fundamental to a subject
Theorems
 NOTE: Click each theorem to take you to another slide with
examples
 If two lines intersect to form a linear pair of congruent angles,
then the lines are perpendicular
 If two sides of two adjacent acute angles are perpendicular, then
the angles are complementary
 If two lines are perpendicular, then they intersect to form four
right angles
Theorems Cont.
 Alternate Interior Angles: If two parallel lines are cut by a
transversal, then the pairs of alternate interior angles are
congruent.
 Consecutive Interior Angles: If two parallel lines are cut by a
transversal, then the pairs of consecutive interior angles are
supplementary
 Alternate Exterior Angles: If two parallel lines are cut by a
transversal, then the pairs of alternate exterior angles are
congruent
Postulates
 Note: Click each postulate to go to another slide with examples
 Parallel Postulate: If there is a line and a point not on the line, then there
is exactly one line through the point parallel to the given line
 Perpendicular Postulate: If there is a line and a point not on the line,
then there is exactly one line through the point perpendicular to the
given line
 Corresponding Angles Postulate: If two parallel lines are cut by a
transversal, then the pairs of corresponding angles are congruent.
Basic Definitions
 NOTE: Click each definition to be directed to another slide with
examples
 Parallel Lines-Two lines that are coplanar and do not intersect
 Skew Lines- Two lines that do not intersect and are not coplanar
 Transversal- A line that intersects two or more coplanar lines at
different points
 Perpendicular Lines- Two lines intersect to form a right angle
Quizlet
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Homework (Print off a copy to bring to class)
Go to quizlet.com
Select create in the upper left-hand corner
Make flashcards
Create an account
View the extra features
Study your flashcards for the quiz tomorrow
Quiz Info
 Out of the 13 definitions only 5 will be on the quiz tomorrow. A
mixture of the names and definitions will be placed in a cup.
From there, you and your classmates will come to the front and
choose one from the cup. If the name or part of the definition is
drawn, the definition must be written (Pretty close to word-forword). If the definition is drawn, the name must be written.
After the 5, students can raise their hands if they wish to
continue with the quiz. It only takes 1 to force the class to
answer more.
Helppp!!
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BI
R
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T
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TC
Ask peers
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P
BD
Read through book
Look on YouTube or Khan Academy
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Come see me before or after school
Click the buttons around the slide for a description of each of the
sections of the PowerPoint (they are abbreviated).
Q
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H
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Quizlet
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QI
BI (Background Info)
 This slide explains the definitions of theorems and
postulates.
P (Postulates)
 The first three of the chapter are given along with
their definitions.
 Click the postulate to take you to another slide where
examples are presented.
T (Theorems)
 The first six theorems of the chapter are given along
with their definitions.
 Click the theorem to take you to another slide where
examples are presented.
TC (Theorems Cont.)
 This slide is a continuation of the previous theorems
slide.
BD (Basic Definitions)
 Four definitions are given. Buttons take you to
another slide where visuals are displayed.
Q (Quiz)
 This slides provides a link to take you to the end of
the presentation where there will be a short quiz.
 The quiz will not be graded, but try your best because
it is great practice for the quiz tomorrow!
QI (Quiz Info)
 This slide provides information on and the
expectations for the quiz the following day.
Qui-zlet (Quizlet)
 This slide provides a brief explanation on how to use
Quizlet and what is expected for the homework for
the following day.
H (Helppp!!)
 This slide presents ways to get extra assistance if
needed.
 It also provides buttons for each of the sections,
which take you to another slide that describes each of
the sections.
 The titles of the buttons are abbreviated by the first
letter of each word.
If two lines intersect to form a linear pair of congruent angles,
then the lines are perpendicular
This theorem is quite significant in geometry. We will use it during
proofs. Click the picture below to see an example of a proof that
we will use this theorem for.
Click
Theorem
to return
to Theorems
If two sides of two adjacent acute angles are perpendicular,
then the angles are complementary
Click Theorem
To return to
Theorems
 Below is a link to a video of a proof that we will solve
in this class
 Video Proof
If two lines are perpendicular, then they intersect to form four
right angles
Click Theorem to return to Theorems
 Using this theorem and the definitions of perpendicular lines and
right angles, you will be able to write different kinds of proofs
for the same situation.
Proof Hints:
• Use definition of perpendicular lines to
find one right angle.
• Use vertical and linear pairs of angles to
find three more right angles.
Alternate Interior Angles: If two parallel lines are cut by a transversal, then
the pairs of alternate interior angles are congruent.
Click TC to return to Theorems Cont.
 Click on the link below to watch a video on the proof
of the theorem.
 AIA
Consecutive Interior Angles: If two parallel lines are cut by a
transversal, then the pairs of consecutive interior angles are
supplementary
Click TC to return to Theorems Cont.
 Click on the link to watch a video on a proof
 CIA
Alternate Exterior Angles: If two parallel lines are cut by a transversal, then
the pairs of alternate exterior angles are congruent
Click TC to return to Theorems Cont.
Parallel Postulate: If there is a line and a point not on the line, then there is
exactly one line through the point parallel to the given line
Click Postulate to return to Postulates
Perpendicular Postulate: If there is a line and a point not on the line, then
there is exactly one line through the point perpendicular to the given line
If we wanted to measure the distance
between a point and a line, we can
employ the Perpendicular Postulate, a
compass, and a straightedge, since
there exists only one perpendicular
line from a point to a line. Click the
button below for an example:
Click Postulate to
return to Postulates
Corresponding Angles Postulate: If two parallel lines are cut by a
transversal, then the pairs of corresponding angles are congruent.
Click Postulate to return to Postulates
 So, in the figure below, if l || m, then angle 1 is
congruent to angle 2.
Parallel Lines-Two lines that are coplanar and do not intersect
Click this button!!!
Click BD to return to Basic Definitions.
Skew Lines- Two lines that do not intersect and are not
coplanar
Click BD to return to Basic Definitions
Transversal- A line that intersects two or more coplanar lines
at different points
Click BD to return to Basic Definitions
Perpendicular Lines- Two lines intersect to form a right angle
Click the button!!
Click BD to return to Basic Definitions
Click this button to return to the theorem
 The next few slides are a short quiz that will not be
graded, but it is great practice for tomorrow’s quiz!
 This quiz is meant to be completed after you have
gone through the full PowerPoint.
 You must answer the questions correctly before
moving on to the next question
 Click the Start button to begin
Start
Question 1
 True or False:
This is the correct definition of parallel lines:
Two lines are parallel if and only if they do not intersect.
 Click True or False
True
False
Return to ?
Move to next ?
*Hint: There is a key word missing from the definition.
Think about the definition of skew lines and how the two differ.
Return to the ?
Question 2
 True or False:
A postulate is a statement that is accepted without
proof and is fundamental to a subject
True
False
Return to the ?
Next ?
*Hint: You’ll find the answer on the Background Info slide
Return to the ?
Question 3
 Fill in the blank:
If two sides of two adjacent acute angles are
perpendicular, then the angles are ________
A. Complementary
B. Supplementary
C. Obtuse
Return to the ?
Next ?
*Hint: Refer to the
Theorems slide
Return to the ?
Question 4
 Which can you add to the blanks to make the statement correct?
If two parallel lines are cut by a transversal, then the pairs of _____ _____
angles are congruent.
I. Consecutive Interior
II. Alternate Exterior
III. Alternate Interior
A. I. and II.
B. II. and III.
C. All three
Return to the ?
Next ?
*Hint: Check out the
theorems
Return to the ?
Question 5
 What makes the following statement incorrect?
A theorem is a statement that hasn’t been proven on
previously established statements like other theorems
and postulates.
A. Proven
B. Statements
C. Hasn’t
Return to the ?
End
*Hint: Is a theorem a
proven statement?
Return to the ?
You have completed the
lesson! Remember to
study for your quiz!
References
http://www.k6-geometric-shapes.com/geometric-terms.html
http://etc.usf.edu/clipart/76000/76015/76015_3_d_lines.htm
http://www.onlinemathlearning.com/pairs-of-lines.html
http://www.themathlab.com/dictionary/swords/swords.htm
http://www.mathsisfun.com/definitions/perpendicular-lines.html
http://www.quia.com/jg/1076804list.html
http://math.tutorvista.com/geometry/transversal-lines.html
http://www.ducksters.com/kidsmath/angles_glossary.php
http://www.mathsisfun.com/geometry/construct-perponline.html
http://www.mathsisfun.com/geometry/construct-perpnotline.html
http://www.mathsisfun.com/geometry/construct-paranotline.html
http://www.docstoc.com/docs/120074625/Given-Angles-1_amp2-are-a-linearpair-Angles-1_amp2-are-congruent
References Cont.
http://grotongeometry.wikispaces.com/Friday+February+29--Version+B
http://mrgiomini.blogspot.com/2013/01/class-topics-010913.html
http://www.sophia.org/proving-angles-are-complementary-with-perpendicularlines/proving-angles-are-complementary-with-perpendicula--5-tutorial
http://www.wyzant.com/help/math/geometry/lines_and_angles/angle_theorems
http://www.youtube.com/watch?v=svprkO5bM88
http://www.mathsisfun.com/geometry/consecutive-interior-angles.html
http://mrwadeturner.pbworks.com/w/page/26527656/Consecutive%20and%20A
lternate%20Exterior%20Angles
http://www.youtube.com/watch?v=GcyIDwMe808
http://doversherborn.comcastbiz.net/highschool/academics/math/baroody/Geom
etryHonors/Class%20Notes/Chapter%205/Lesson5-3/Lesson5-3.html
http://hotmath.com/hotmath_help/topics/corresponding-angles-postulate.html
http://en.wikipedia.org/wiki/Parallel_postulate
References Cont.
http://www.goodlightscraps.com/congrats.php
http://www.noodle.org/learn/details/231602/example-of-something-that-goeswrong-in-the-lab
http://www.sodahead.com/living/can-you-please-tell-me-something-aboutcanada/question-1756107/?link=ibaf&q=wrong+answer
http://www.broward.org/Kids/EnvironmentalKidsClub/Pages/WrongAnswer.aspx
http://pyhong.blogspot.com/2010/03/thumbs-down-to-me.html
http://tracemypreps.com/2013/01/03/review-of-goals-for-2012/stop-go-backtry-again/
http://www.keepcalm-o-matic.co.uk/p/keep-calm-and-try-again-36/
References Cont.
http://www.lavenir-jit.com/quiz-competition.html
http://www.funscrape.com/Scraps.aspx?CatName=Good+Job
http://www.grandprofile.com/Myspace_Comments/Congratulations_Comments/
http://www.clker.com/clipart-correct-mark-4.html
https://smarttan.com/news/index.php/headline-story-smart-tan-memberresponds-in-print-on-the-radio-to-false-iarc-report/
http://phsmath.pbworks.com/w/page/16606090/FrontPage
http://support.prometheanplanet.com/server.php?show=nav.17545
http://www.gpsmagazine.com/2009/11/tomtom_one_140_s_review.php?page=4
http://simonhowells.typepad.com/my-blog/2010/02/new-blogpost-quizlet.html
http://berkscountynbems.homestead.com/Berks-NBEMS-Help-Page.html