Transcript 8 Lesson 8.1 cont

I am playing a game with
these rules:
If I roll a fair die and get a factor of 6, then I
get 3 points. If I roll a 5, I get 4 points. If I
roll a factor of 4, then I get x points.
(1) Find the value of x so that the game is fair.
(2) Find P(3, even, 4); P(odd, 4, odd)
(3) True or false? P(even, 3) = P(3, even)
Agenda
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Go over warm up.
Go over homework 7.3 and 7.4
Geometry: Exploration 8.1.
Play with protractors.
Exploration 8.6.
More practice problems.
Assign homework.
Homework 7.3
• 4 red socks, 4 blue socks, no replace
• 2a P(r, r) or P(b, b)
• 2b
P(match)
• 2c
P(4 red) or P(4 blue)
Homework 7.3
• 8. 2 four-sided dice. List the
outcomes. P(most common sum)
• 13.
Roll a double 3 times in a row.
• P(1st double) P(2nd double) P(3rd double)
Homework 7.4
• 2.
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• 7.
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Candidates A, B, C, D.
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12 kids, 3-member groups.
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Homework 7.4
• 8
9 players, 5 starting
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____ ____ ____ ____ ____
• 13 2 apps., 4 main, 3 dessert
• Possible dinners? ____ ____ ____
• 3 salad dress, 4 flavors ice cream
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____ ____ ____
What is Geometry?
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Points, lines, planes, angles
Curves, Polygons, circles, polyhedra, solids
Congruence, similarity
Reflections, rotations, translations, tessellations
Distance, Perimenter, Area, Surface Area, Volume,
Temperature, Time, Mass, Liquid vs. Solid Capacity
• Above, below, beside, left, right, upside-down,
perception, perspective
Geometry
• Notice that nowhere on the previous list is the word
“proof.”
• An example shows that something is true at least
one time.
• A counter-example shows that something is not true
at least one time.
• A proof shows that something is true (or not true) all
of the time.
• This is what all of mathematics is based upon, not
just geometry.
Geometry
• If we believe something to be true…
– Assumption/Axiom/Postulate
– Conjecture/Hypothesis
– Definition
• If we can prove something to be true…
– Theorem
– Property
These words are not interchangeable!!
Some words are hard to
define
• Describe the color red to someone.
• Can you define the color red?
• Can you define or describe the color
red to someone who is blind?
Some words are hard to
define
• Point: a dot, a location on the number line or
coordinate plane or in space or time, a pixel
• Line: straight, never ends, made up of
infinite points, has at least 2 points
• Plane: a flat surface that has no depth that is
made up of at least 3 non-collinear points.
• We say these terms are undefined.
With undefined terms, we
can describe and define…
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Segment
Ray
Angle
Collinear points
Coplanar lines
Intersecting lines
Skew lines
Concurrent lines
Symbols
• We use some common notation.
• Line, line segment, ray: 2 capital letters
AB
AB
AB
BA or t
• Point: 1 capital letter D
• Plane: 1 upper or lower case letter Pp
• Angle: 3 capital letters with the vertex in the center,
or the vertex letter or number  ACD
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B
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A
p
Try these
Name 3 rays.
Name 4 different angles.
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Name 2 supplementary angles.
Name a pair of vertical angles.
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Name a pair of adjacent angles.
Name 3 collinear points.
B
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E
G
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Try these
Name 2 right angles.
Name 2 complementary angles.
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Name 2 supplementary angles.
Name 2 vertical angles.
True or false: AD = DA.
If m  EDH = 48˚, find m  GDC. •B
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D
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Euclid’s Postulates
• 1. A straight line segment can be drawn
joining any two points.
• 2. Any straight line segment can be
extended indefinitely in a straight line.
• 3. Given any straight line segment, a
circle can be drawn having the segment as
radius and one endpoint as center.
• 4. All right angles are congruent.
Euclid’s Fifth Postulate
• 5. If two lines are drawn which intersect a
third in such a way that the sum of the inner
angles on one side is less than two right
angles, then the two lines inevitably must
intersect each other on that side if extended
far enough. This postulate is equivalent to
what is known as the parallel postulate.
A
C
Try these
• Assume lines l, m, n
are parallel.
• Copy this
diagram.
• Find the value of
each angle.
l
Exploration 8.1
• Do this individually
• Part 4 #1
• Copy or cut and tape the figures so that
the groups are easy to distinguish.
• Describe the attribute (characteristic) of
each group.
• Share results with the rest of your table.
How did you group the
polygons?
• For kids… talk about attributes
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Shape: # sides, special quadrilaterals
Convex or non-convex
(1 or 2) Pair of parallel sides
(1 or 2) Pair of congruent sides
(1 or 2) Pair of perpendicular sides
Nothing special about it.
Cannot do any proof or justification if kids can’t
classify and describe similarities and differences.
How do I use a protractor?
I forgot!
• Line up the center and line.
TIF
F (U
Q
are nc o uic k T
nee mpr ime
ded ess ™ a
to s ed) d nd a
ee t eco
hi s mpr
pic t es s
130˚
ure or
.
50˚
Can you…
• Sketch a pair of angles whose
intersection is:
a. exactly two points?
b. exactly three points?
c. exactly four points?
• If it is not possible to sketch one or
more of these figures, explain why.
Use Geoboards
• On your geoboard, copy the given segment.
• Then, create a parallel line and a
perpendicular line if possible. Describe how
you know your answer is correct.
Exploration 8.6
• Do part 1 using the pattern blocks--make sure your
justifications make sense.
• You may not use a protractor for part 1.
• Once your group agrees on the angle measures for
each polygon, trace each onto your paper, and
measure the angles with a protractor.
• List 5 or more reasons for your protractor measures
to be slightly “off”.
More practice problems
• Given m // n.
• T or F:  7 and  4
3
are vertical.
2
1
• T or F:  1   4
• T or F:  2   3
• T or F: m  7 + m  6 = m  1
• T or F: m  7 = m  6 + m  5
• If m  5 = 35˚, find all the angles you can.
6
7
4
5
m
n
More practice problems
• Think of an analog clock.
• A. How many times a day will the minute hand be
directly on top of the hour hand?
• B. What times could it be when the two hands
make a 90˚ angle?
• C. What angle do the hands make at 7:00? 3:30?
2:06?
More practice problems
• Sketch four lines such that three are
concurrent with each other and two are
parallel to each other.
True or False
• If 2 distinct lines do not intersect, then they are
parallel.
• If 2 lines are parallel, then a single plane contains
them.
• If 2 lines intersect, then a single plane contains them.
• If a line is perpendicular to a plane, then it is
perpendicular to all lines in that plane.
• If 3 lines are concurrent, then they are also coplanar.
Homework
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Due Thursday:
Section 8.1--do all, turn in the bold.
p. 518 #2, 5, 9, 10
Read section 8.2.