Geometry 28/29 November, 2012
1) Place binder and book on your desk.
2) Do Warm Up: (back top)
a) What property states that BD = BD?
b) What does CPCTC mean?
c) Briefly define and sketch median.
d) Draw a scalene triangle
on patty paper.
Construct all three medians
by folding to find midpoints, then
drawing in the medians with a pencil.
median
the segment connecting the vertex
of a triangle to the midpoint of its
opposite side
median
Need to come and take test TODAY
P2- Vincent, Jordan, Lizeth
P5- GG
objective
Students will apply triangle properties, triangle
congruency shortcuts and CPCTC to do twocolumn and flow chart proof and explore
polygon angle sums.
Students will take notes, work independently
and collaboratively and present to the class.
Homework
Due November 30- sign up for Khan Academy and add
me as your coach
Choose 5 of the topics listed on the handout and
practice until you can get 10 correct
(Linear Equations, Linear Functions, Polygons
Triangle Congruency, Basic Triangle Proof)
Shuttling Around- REVISIONS accepted through
November 30th!
MAKE SURE ANY CHANGES ARE EXTREMELY OBVIOUS 
I don’t have time to re-read your whole project!! 
(use different color, notes, etc.)
The Congruence Shortcut
Conjectures
 SSS
correspondence
 ASA
correspondence
 SAS
correspondence
 AAS
correspondence
 HL
correspondence
 SSA
correspondence
 AAA
correspondence
CPCTC…
If two triangles are congruent, then
Corresponding Parts of those Congruent Triangles are
Congruent CPCTC
You must make sure you have
CORRESPONDING PARTS SAME RELATIVE POSITION!!!
HINTS– Use colored pencils to mark corresponding parts.
Mark all info you know on the figure.
Redraw triangles separately,
and facing the same direction.
Extend lines or draw additional lines to
make triangles.
Use ARROWS.
Finish Classwork? END OF CLASS VIDEO
http://www.youtube.com/watch?feature=endscreen&v=_L8u8io6n2A&NR=1
Flow Chart Proof
1. Mark known information on a sketch.
2. Start by writing the given information.
3. Write what you are trying to prove or show
on the right.
4. Fill in the other boxes working backwards
and forwards as needed.
ASK:
what do I need to know in order to claim the conclusion
is true?
what must I show to prove the intermediate result?
Proofs– HOW?
See page 237- 238
See example A- paragraph proof
example B- flowchart proof
Compare the paragraph proof in Ex. A with the
flowchart proof in Ex. B.
What similarities and differences are there?
What is the advantage of each format?
Finish Two Column Proof Handout
Finish handout from yesterday.
Think- work silently for 5 minutes
Pair- check with a partner
Share- whole class discussion
FINISH 4.6 handout, CPCTC
1 – 9, 12
Polygons
The word
‘polygon’ is a
Greek word.
Poly means
many and
gon means
angles.
Polygons
• The word polygon means
“many angles”
• A two dimensional object
• A closed figure
Polygons
More about Polygons
• Made up of three or more
straight line segments
• There are exactly two sides
that meet at each vertex
• The sides do not cross each
other
Polygons
Examples of Polygons
Polygons
These are not Polygons
Polygons
Terminology
Side: One of the line
segments that make up a
polygon.
Vertex: Point where two sides
meet.
Polygons
Vertex
Side
Polygons
• Interior angle: An angle
formed by two adjacent sides
inside the polygon.
• Exterior angle: An angle
formed by two adjacent sides
outside the polygon.
Polygons
Exterior angle
Interior angle
Polygons
WRITE THIS IN YOUR NOTES
Exterior angle
Vertex
Side
Diagonal
Polygons
Interior angle
An exterior angle of a polygon is
formed by extending one side of the polygon.
Angle CDY is an exterior angle to angle CDE
B
A
C
F
2
E
D
1
Y
Exterior Angle + Interior Angle of a regular polygon =180
Polygons
0
1200
600
600
1200
Polygons
600
1200
Is there a connection between
the number of sides,
the number of triangles and
the sum of the measures of
the angles in a polygon?
Work with your group to complete
Polygon Angle Sum Measures
Polygons
No matter what type of
polygon we have, the sum
of the exterior angles is
ALWAYS equal to 360º.
Sum of exterior angles =
360º
Polygons
Polygons
Term
Polygon
Sum
Conjecture
Definition
The sum of the measures of
the interior angles of an
n-gon is
180  n  2 
0
Exterior
angle sum
conjecture
For any polygon, the
sum of the measures of
a set of external angles
is 3600
Equiangular
Polygon
Conjecture
Each interior angle of an
equiangular n-gon
1800  n  2 
n
Example
Sum of interior
angles
1800  n  2 
1800  n  2 
n
debrief
What patterns did you notice with polygon
interior angles?
What patterns did you notice with polygon
exterior angles?