Download x 2 , y 2 - Shope-Math

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.
m1  m2  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?