Transcript Geometry-1 Oct 2012- 2.6 Parallel Line - Shope-Math

Honors Geometry 1 Oct 2012
1) Place binder and text on your desk.
2) Place everything from RIGHT side of
folders into correct section of your binder.
3) Warm-up (TOP front)
Think: Vertical or linear pair?
Set up equation and
solve for x, justifying each step
2x  5
4 x  11
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
reasoning
observing data, recognizing patterns,
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
interior
angles (AIA)
inside the two lines on opposite
side of transversal
alternate
exterior
angles (AEA)
outside the two lines on opposite side of
transversal
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)
alternate exterior angles
(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 1800
1 2
2. Vertical angles are congruent
1
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.
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?