geometry 28/29 november, 2012
DESCRIPTION
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 - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Geometry 28/29 November, 2012](https://reader036.vdocuments.mx/reader036/viewer/2022081520/56815ac6550346895dc893f8/html5/thumbnails/1.jpg)
Geometry 28/29 November, 20121) 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, thendrawing in the medians with a pencil.
![Page 2: Geometry 28/29 November, 2012](https://reader036.vdocuments.mx/reader036/viewer/2022081520/56815ac6550346895dc893f8/html5/thumbnails/2.jpg)
medianthe segment connecting the vertex
of a triangle to the midpoint of its opposite side
median
![Page 3: Geometry 28/29 November, 2012](https://reader036.vdocuments.mx/reader036/viewer/2022081520/56815ac6550346895dc893f8/html5/thumbnails/3.jpg)
Need to come and take test TODAY
P2- Vincent, Jordan, LizethP5- GG
![Page 4: Geometry 28/29 November, 2012](https://reader036.vdocuments.mx/reader036/viewer/2022081520/56815ac6550346895dc893f8/html5/thumbnails/4.jpg)
objective
Students will apply triangle properties, triangle congruency shortcuts and CPCTC to do two-column and flow chart proof and explore polygon angle sums.
Students will take notes, work independently and collaboratively and present to the class.
![Page 5: Geometry 28/29 November, 2012](https://reader036.vdocuments.mx/reader036/viewer/2022081520/56815ac6550346895dc893f8/html5/thumbnails/5.jpg)
HomeworkDue 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.)
![Page 6: Geometry 28/29 November, 2012](https://reader036.vdocuments.mx/reader036/viewer/2022081520/56815ac6550346895dc893f8/html5/thumbnails/6.jpg)
The Congruence Shortcut Conjectures
SSS correspondence
ASA correspondence
SAS correspondence
AAS correspondence
HL correspondence
SSA correspondence
AAA correspondence
![Page 7: Geometry 28/29 November, 2012](https://reader036.vdocuments.mx/reader036/viewer/2022081520/56815ac6550346895dc893f8/html5/thumbnails/7.jpg)
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 VIDEOhttp://www.youtube.com/watch?feature=endscreen&v=_L8u8io6n2A&NR=1
![Page 8: Geometry 28/29 November, 2012](https://reader036.vdocuments.mx/reader036/viewer/2022081520/56815ac6550346895dc893f8/html5/thumbnails/8.jpg)
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?
Flow Chart Proof
![Page 9: Geometry 28/29 November, 2012](https://reader036.vdocuments.mx/reader036/viewer/2022081520/56815ac6550346895dc893f8/html5/thumbnails/9.jpg)
Proofs– HOW?
See page 237- 238See 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?
![Page 10: Geometry 28/29 November, 2012](https://reader036.vdocuments.mx/reader036/viewer/2022081520/56815ac6550346895dc893f8/html5/thumbnails/10.jpg)
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
![Page 11: Geometry 28/29 November, 2012](https://reader036.vdocuments.mx/reader036/viewer/2022081520/56815ac6550346895dc893f8/html5/thumbnails/11.jpg)
PolygonsThe word
‘polygon’ is a Greek word.
Poly means many
and gon means angles.
![Page 12: Geometry 28/29 November, 2012](https://reader036.vdocuments.mx/reader036/viewer/2022081520/56815ac6550346895dc893f8/html5/thumbnails/12.jpg)
Polygons
Polygons
• The word polygon means “many angles”
• A two dimensional object
• A closed figure
![Page 13: Geometry 28/29 November, 2012](https://reader036.vdocuments.mx/reader036/viewer/2022081520/56815ac6550346895dc893f8/html5/thumbnails/13.jpg)
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
![Page 14: Geometry 28/29 November, 2012](https://reader036.vdocuments.mx/reader036/viewer/2022081520/56815ac6550346895dc893f8/html5/thumbnails/14.jpg)
Examples of Polygons
Polygons
![Page 15: Geometry 28/29 November, 2012](https://reader036.vdocuments.mx/reader036/viewer/2022081520/56815ac6550346895dc893f8/html5/thumbnails/15.jpg)
These are not Polygons
Polygons
![Page 16: Geometry 28/29 November, 2012](https://reader036.vdocuments.mx/reader036/viewer/2022081520/56815ac6550346895dc893f8/html5/thumbnails/16.jpg)
Terminology
Side: One of the line segments that make up a polygon.
Vertex: Point where two sides meet.
Polygons
![Page 17: Geometry 28/29 November, 2012](https://reader036.vdocuments.mx/reader036/viewer/2022081520/56815ac6550346895dc893f8/html5/thumbnails/17.jpg)
Vertex
Side
Polygons
![Page 18: Geometry 28/29 November, 2012](https://reader036.vdocuments.mx/reader036/viewer/2022081520/56815ac6550346895dc893f8/html5/thumbnails/18.jpg)
• 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
![Page 19: Geometry 28/29 November, 2012](https://reader036.vdocuments.mx/reader036/viewer/2022081520/56815ac6550346895dc893f8/html5/thumbnails/19.jpg)
Interior angle
Exterior angle
Polygons
![Page 20: Geometry 28/29 November, 2012](https://reader036.vdocuments.mx/reader036/viewer/2022081520/56815ac6550346895dc893f8/html5/thumbnails/20.jpg)
WRITE THIS IN YOUR NOTES
Interior angle
Diagonal
Vertex
Side
Exterior angle
Polygons
![Page 21: Geometry 28/29 November, 2012](https://reader036.vdocuments.mx/reader036/viewer/2022081520/56815ac6550346895dc893f8/html5/thumbnails/21.jpg)
An exterior angle of a polygon is formed by extending one side of the polygon.
Angle CDY is an exterior angle to angle CDE
Exterior Angle + Interior Angle of a regular polygon =1800
DEY
B
C
A
F
12
Polygons
![Page 22: Geometry 28/29 November, 2012](https://reader036.vdocuments.mx/reader036/viewer/2022081520/56815ac6550346895dc893f8/html5/thumbnails/22.jpg)
1200
1200
1200
600 600
600
Polygons
![Page 23: Geometry 28/29 November, 2012](https://reader036.vdocuments.mx/reader036/viewer/2022081520/56815ac6550346895dc893f8/html5/thumbnails/23.jpg)
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
![Page 24: Geometry 28/29 November, 2012](https://reader036.vdocuments.mx/reader036/viewer/2022081520/56815ac6550346895dc893f8/html5/thumbnails/24.jpg)
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
![Page 25: Geometry 28/29 November, 2012](https://reader036.vdocuments.mx/reader036/viewer/2022081520/56815ac6550346895dc893f8/html5/thumbnails/25.jpg)
Term Definition Example
Polygon Sum
Conjecture
The sum of the measures of the interior angles of an
n-gon is
Sum of interior angles
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
Polygons
0180 2n 0180 2n
0180 2n
n
0180 2n
n
![Page 26: Geometry 28/29 November, 2012](https://reader036.vdocuments.mx/reader036/viewer/2022081520/56815ac6550346895dc893f8/html5/thumbnails/26.jpg)
debriefWhat patterns did you notice with polygon interior angles?
What patterns did you notice with polygon exterior angles?