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Honors Geometry 28/29 Sept 2011 Take papers from your folder and put them in the correct section in your binder. Note- remove everything from both sides EXCEPT keep your warm up paper in the left pocket through the week Check your homework Warm-up- silently please angle chase- do pg. 166: 17 handout: list angles in alphabetical order give reasons/ show brief work for ALL (ie CA, 180 – a =, a = c = ___ VA, etc.) Objective Students will use inductive reasoning to find the next term in a number or picture pattern. Students will take notes, do an investigation and work collaboratively. Developing the slope formula (x2, y2) y2 y2-y1 y1 y x1 y1 x2 y2 slope formula (x1, y1) x1 (x2-x1) x x2 y2 y1 m x2 x1 (y2-y1) H o m e w o r k d u e T O D AY pg. 136: 1 – 8; pg. 142: 24 - 25 Homework due Monday section 2.1: 3 – 15 odds only CHALLENGE: pg. 101: Puzzling Patterns UPCOMING due dates Quiz- FridayVocab/Naming/Labling Angle Conjectures Angle “Chase” 3 conjectures: 1. Linear pairs add up to 1800 1 2. Vertical angles are congruent 1 2 2 3. If two parallel lines are cut by a transversal, then corresponding angles (CA)are CONGRUENT, alternate interior angles (AIA)are CONGRUENT and alternate exterior angles (AEA)are CONGRUENT. NOTE- this is true ONLY when transversal cuts PARALLEL lines!! 1 2 1 2 1 2 converse of parallel lines conjecture If 2 lines are cut by a transversal to form congruent pairs of CA, AIA and AEA, then the lines are parallel same side interior angle (SSIA) conjecture If a transversal cuts two parallel lines, then same side interior angles are 1 supplementary. m1 m2 180 2 If a conjecture and its converse are if and only if both true, we can use the words “if and only if” “If x, then y AND if y, then x” could be stated as “x” if and only if “y” example: CA, AIA, AEA and SSIA are congruent if and only if the lines cut by a transversal are parallel. what do you know about angles in this figure? Vertical or Linear pair? solve for x, justifying each step 5x 6 2x 12 Easy for you??? Try page 133 # 15 and 16 Vertical or linear pair? solve for x, justifying each step 2x 5 4 x 11 Easy for you??? Try page 133 # 15 and 16 set up and solve for x, justifying each step 3x 15 2x 5 same side interior conjecture: if a transversal cuts two parallel lines, then same side interior (SSI) angles are supplementary. a review look in your notes– what is inductive reasoning? give an example Consider the sequence: 2, 4, 7, 11,… Make a conjecture about the rule for generating this sequence. If the pattern continues, then……. pg. 98 Shape Shifters Silently read the investigation, steps 1 – 5 to yourself Check in- what are we trying to do? Silently do the investigation Discuss with your group READ paragraph after the investigation!! FINISHED: do problems 4 – 14 EVENS Be ready to share your work with the class Debrief- EQ what did you learn today? What was easy for you? What did you like? What was difficult? Is there something I could do to help you?