2) do Warm Up (Bottom front) a) Briefly define ALTITUDE and make a sketch

1. Geometry 33 November, 2012 1) Place binder and text on your desk. 2) do Warm Up (Bottom front) a) Briefly define ALTITUDE and make a sketch Does the altitude BISECT the opposite side? b) Draw a SCALENE triangle on patty paper and label the vertices, A, B and C. CONSTRUCT an altitude from B to the opposite side by folding.

2. objective Students will apply triangle properties, congruency shortcuts and CPCTC to do two-column and flow chart proof. Students will take notes, work independently and collaboratively and present to the class.

3. Homework Due November 30- sign up for Khan Academy and add me as your coach Choose 5 topics from the sections 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.)

4. SSS correspondence • ASA correspondence • SAS correspondence • AAS correspondence • HL correspondence • SSA correspondence • AAA correspondence The Congruence Shortcut Conjectures

5. 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!!! STRATEGIES– 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. Music Video http://www.youtube.com/watch?feature=endscreen&v=_L8u8io6n2A&NR=1

6. altitude the perpendicular segment from a vertex to the opposite side or a line containing the opposite side

7. Below is another partially drawn triangle. In this case, AB has been drawn and two angles have been created. If you extend two sides from , how many different triangles can you create? ONE! ASA is a triangle congruency shortcut!!

8. Identify Angle Side Angle Relationships Which pair of triangles on the illustrates an angle side angle relationship? http://www.mathwarehouse.com/geometry/congruent_triangles/angle-side-angle-postulate.php, retrieved Nov 21, 2012

9. proof • Given: is an altitude to , ⦟ABC ⦟DBC Prove ΔBCA  ΔBCD and Start by marking given congruencies and other information on your diagram. Plan your proof. Is there a triangle congruency shortcut you can use?

10. Given: is an altitude to , ⦟ABC ⦟ DBC ⦟ABC ⦟ DBC is an altitude to m⦟ACB=m⦟DCB = 90⁰ reflexive property ASA Congruence CPCTC

12. Definitions of special Quadrilaterals Quadrilateral – a four sided polygon Kite- a quadrilateral with two distinct pairs of consecutive congruent sides. Parallelogram- a quadrilateral with 2 pairs of parallel sides.

13. practice Do Two- Column Proof Handout. Think– silently for 5 minutes Pair– work with a partner Share- whole class discussion Be ready to present to the class.

14. debrief What is easy about proof? What might some students find to be confusing? What do you need to practice?