Transcript Alternate Interior Angle Theorem

Alternate Interior Angle
Theorem
By: Miguel Reyes
Whats a Alternate Interior
Angle Theorem?
• If two parallel lines are cut by a
transversal, the alternate interior angles
are congruent.
Example
The End
Complementary and
Supplementary angles
By Ryan Herlihy
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Complementary angles
• These are 2 angles that add up to 90º
• It is 2 adjacent angles or 2 non adjacent angles adding up to 90º
Practice Problems
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+5
Ex:Find x
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Since this is a complementary angle it equals
90º
This means that:
x+5+45=90º
-50 -50
x = 40º
Supplementary angles
– All supplementary angles are 2 angles that add up to 180º
– It can be adjacent or non adjacent angles adding up to 180º
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________________Practice Problems_________________
•
Find x if <1 and <2
are supplementary
<1 = 57º
<2 = x+33
57+x+33=180
-90
-90
X = 90º
•
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X+25
Find x. if line wx is supplementary
X+25+60=180
-85
-85
x = 95
Helpful links
• http://www.mathleague.com/help/geome
try/angles.htm
http://www.mathwarehouse.com/geometry/angle/su
pplementary-angles.php
http://www.aaaknow.com/geo-comp-or-sup.htm
Corresponding Angles
Postulate
When two parallel lines are cut
by a transversal, the resulting
corresponding angles are
congruent
Properties
• Any angles that are corresponding to
each other are congruent
Example Problems
•
•
•
•
1. What angle is angle 1 congruent to?
2. What angle is congruent to angle 6?
3. Are angle 2 and 4 congruent?
4. What angle is congruent to angle 7?
•
•
•
•
•
Answers:
1. Angle 3
2. Angle 8
3. Yes
4. Angle 5
Web Links
• http://hotmath.com/hotmath_help/topics/corre
sponding-angles-postulate.html
• http://www.mathwarehouse.com/geometry/an
gle/transveral-and-angles.php
• http://en.wikibooks.org/wiki/Geometry/Postula
tes_%26_Definitions
Segment Addition Postulate
• If a segment is divided into two smaller
segments, the sum of the mini two must
equal the length of the whole segment.
Rules, Properties, and
Formulas
• If A, B and C are collinear, and B is
between A and C, then AB + BC = AC.
Examples
• Point L is between points N and M. If NL= 6x-5, LM=
2x+3, and NM = 30, find x, NL, and LM
Answer:
x=4
• Point W is between R and S. If RS = 7x+8, RW = 4x3, and WS = 6x+2, find x, RW, WS, and RS.
Answer: x= 3
• B is between A and C. Find the value of x and the
measure of BC if: AB = 3, BC = 4x + 1, AC = 8.
Answer: x=1
Web Links
• http://www.gradeamathhelp.com/segme
nt-addition-postulate.html
• http://www.coursenotes.org/Geometry/Segments_and_Ra
ys/Segment_Addition_Postulate
• http://www.tutorvista.com/math/segment
-addition-postulate-definition
Law of Syllogism
The Law of Syllogism is used when writing a
deductive statement. It states:
A = B
B = C
A = C
My goal is to help jog your memory about the
Law and how to use it.
Steps to create:
• Step 1: create a simple if-then statement.
• Step 2: Use the then portion as the new if and relate
that to something else.
• Step 3: Use the first if portion and relate that to the
final then.
Examples on Next Slide
Examples:
• If it is snowing, then it is cold out. If it is cold
out then it is Winter. If it is snowing, then it is
Winter.
• If the weather is fine, then school is open. If
school is open, kids will go to school. If the
weather is fine, kids will go to school.
• If the Jets beat the Steelers, then they will
advance. If they advance, they will go to the
Super Bowl. If the Jets beat the Steelers, they
will go to the Super Bowl.
http://www.freelawanswer.com/law/31713-freelawanswer.html