Think: Vertical or linear pair? Set up equation and solve for x, justifying each step 1) Place binder and text on your desk. everything 2) Place everything.

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Presentation transcript:

Think: Vertical or linear pair? Set up equation and solve for x, justifying each step 1) Place binder and text on your desk. everything 2) Place everything from RIGHT side of folders into correct section of your binder. 3) Warm-up (TOP front) Honors Geometry 1 Oct 2012

objective Students will recognize and find missing angle measures.TUTORING: Monday 3 – 3:45 Thursday 1:30 – 2:15 HOMEWORK due Tuesday: pg. 131: 1- 6, 9, 14 – 16 (sketches, K’s, W’s, explain!)

words to know- add to vocab inductive observing data, recognizing patterns, reasoning then making a generalization conjecture the generalization; “if…then….” examples? converse switch the “if….then…” parts ex. if two angles are vertical angles, then they are congruent  converse would be (which is not true) if two angles are congruent, then they are vertical angles

transversal a line intersecting 2 or more lines angles formed by a transversal intersecting 2 lines: corresponding same relative position angles (CA) alternate inside the two lines on opposite interior side of transversal angles (AIA) alternate outside the two lines on opposite side of exterior transversal angles (AEA)

TRANSVERSAL

corresponding angles (CA) 1 and 5 2 and 6 3 and 7 4 and 8

alternate interior angles (AIA) 3 and 6 4 and 5

alternate exterior angles (AEA) 2 and 7 1 and 8

In your vocabulary notes, sketch the figure and identify: transversal corresponding angles (CA) alternate interior angles (AIA) (AIA) alternate exterior angles (AEA) (AEA)

section 2.6 Investigations what if the two lines ARE parallel? Investigation 1- steps 1 and 2- whole class NOTE– “paper” = notebook paper “patty paper” = “patty paper” compare your results with your group so what do you think? Verbally discuss the three conjectures (CA, AIA and AEA) on page 129 with your group

what about the converse? Investigation 2- pg. 130 “paper” = notebook paper “patty paper” = “patty paper” whole class

3 conjectures: 1.Linear pairs add up to Vertical angles are congruent 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!!

If converse of If 2 lines are cut by a transversal parallel lines to form congruent pairs of then conjecture CA, AIA and AEA, then the are parallel. lines are parallel.

NOTE proof format for “angle chases” see handout Use for all angle chases 1) start with identifying the given angles on your diagram 2) first steps for proof are writing what is given 3) follow handout!

finish ALL students must complete- if not completed in class, FINISH for HOMEWORK- due Friday! (there will be other homework assigned) 1) Angle Pair Relationship Worksheet 2) 2.5 Angles Worksheet 3) 2.6 Handout Be ready to share your results with the class

debrief what have you learned? what is easy? what might be confusing to some students?

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