think: vertical or linear pair? set up equation and solve for x, justifying each step 1) place...
DESCRIPTION
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 anglesTRANSCRIPT
Think: Vertical or linear pair? Set up equation and
solve for x, justifying each step
2 5x
1) Place binder and text on your desk.2) Place everythingeverything from RIGHT side of folders into correct section of your binder.3) Warm-up (TOP front)
4 11x
Honors Geometry 1 Oct 2012
objectiveStudents will recognize and find missing angle measures.TUTORING:TUTORING:Monday 3 – 3:45Monday 3 – 3:45Thursday 1:30 – 2:15Thursday 1:30 – 2:15HOMEWORK due Tuesday: HOMEWORK due Tuesday: pg. 131: 1- 6, 9, 14 – 16 (sketches, K’s, W’s, explain!)pg. 131: 1- 6, 9, 14 – 16 (sketches, K’s, W’s, explain!)
words to know- add to vocabinductive 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 positionangles (CA)
alternate inside the two lines on oppositeinterior side of transversalangles (AIA)
alternate outside the two lines on opposite side ofexterior transversalangles (AEA)
TRANSVERSALTRANSVERSAL
corresponding angles (CA)
1 and 5 2 and 63 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:
transversalcorresponding angles (CA)corresponding angles (CA)alternate interior angles alternate interior angles (AIA)(AIA)alternate exterior angles alternate exterior angles (AEA)(AEA)
section 2.6 Investigationswhat if the two lines ARE parallel?
Investigation 1- steps 1 and 2- whole classNOTE– “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:1.1.Linear pairs add up to 180Linear pairs add up to 18000 2.2.Vertical angles are congruentVertical angles are congruent
3. If two 3. If two parallelparallel lines are cut by lines are cut by a a transversal, then transversal, then corresponding corresponding anglesangles (CA)are CONGRUENT (CA)are CONGRUENT, , alternate interior anglesalternate interior angles (AIA)are CONGRUENT (AIA)are CONGRUENT and and alternate exterior anglesalternate exterior angles (AEA)are CONGRUENT.(AEA)are CONGRUENT.NOTE- this is true ONLY when NOTE- this is true ONLY when transversal cuts transversal cuts PARALLELPARALLEL lines!!lines!!
1 2
12
12
1 2
1
2
converse of IfIf 2 lines are cut by a transversalparallel lines to form congruent pairs ofconjecture CA, AIA and AEA, thenthen the lines are parallel.are parallel.
NOTE proof format for “angle chases”
• see handout• Use for all angle chases1) start with identifying the given angles on your
diagram2) first steps for proof are writing what is given3) 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 Worksheet2) 2.5 Angles Worksheet3) 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?