Geometry 28/29 November, ) 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. 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 two- column 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 me as your coach Choose 5 of the topics listed on the handout and Choose 5 of the topics listed on the handout and practice until you can get 10 correct practice until you can get 10 correct (Linear Equations, Linear Functions, Polygons (Linear Equations, Linear Functions, Polygons Triangle Congruency, Basic Triangle Proof) Triangle Congruency, Basic Triangle Proof) Shuttling Around- REVISIONS accepted through November 30 th ! 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

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

Proofs– HOW? See page 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 gon Poly means many and gon means angles.

Polygons “many angles”The word polygon means “many angles” two dimensionalA two dimensional object closedA closed figure

More about Polygons line segmentsMade up of three or more straight line segments exactly two sides that meet at each vertexThere are exactly two sides that meet at each vertex sides do not crossThe 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

Interior angle Exterior angle Polygons

WRITE THIS IN YOUR NOTES Interior angle Diagonal Vertex Side Exterior angle Polygons

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 =180 0 D E Y B C A F 1 2 Polygons

Polygons

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

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 Equiangular Polygon Conjecture Each interior angle of an equiangular n-gon Polygons

debrief What patterns did you notice with polygon interior angles? What patterns did you notice with polygon exterior angles?