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## Bellringer

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### Title: Section 2.4: Use Postulates and Diagrams Author: Bruce Feist Last modified by: Bruce D Feist Created Date: 9/28/2011 3:20:14 AM Document presentation format – PowerPoint PPT presentation

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Title: Bellringer

1
Bellringer
• Block 2 Quizlets VENN and TRT. You have 5
minutes.
• Blocks 1 3
• Write a logic table that you think describes p
and q both being true at the same time (AND).
Use the symbol .
• Write a logic table that you think describes at
least one of them (p q) being true (OR). Use
the symbol .
• Write a truth table that finds the values for p
-gt q and p q. Do you see a relationship? Are
they equivalent?
• Solutions are on the next slide.

2
Bellringer Solutions
T F
T T F
F F F
T F
T T T
F T F
p q q p -gt q p q
T T F T F
T F T F T
F T F T F
F F T T F
p -gt q and p q arent equivalent theyre
opposites. Whenever one is true, the other is
false. This makes sense p q means that the
hypothesis is true, but the conclusion is
false. Thats the only time that p -gt q is false.
3
Use Postulates and Diagrams
• Section 2.4

4
Objectives Announcements
• Add new postulates to our repertoire
• Recognize the use of postulates in diagrams
• Diagram postulates
• HW for next time page 134-136, 1-13.
• Test on 2.1-2.4 next class! We will review
before the test.

5
Old Postulates
• From Chapter 1
• Postulate 1 Ruler Postulate
• Postulate 2 Segment Addition Postulate
• A B C AB BC AC
• Postulate 3 Protractor Postulate
• Postulate 4 Angle Addition Postulate
• m?AVB m?BVC m?AVC

A
B
V
C
6
New Postulates (Point, Line, Plane)
• 5 Through every two points, there is exactly
one line.
• 6 Every line contains at least two points.
• 7 If two lines intersect, their intersection is
exactly one point.
• 8 Through any three noncollinear points, there
exists exactly one plane.
• 9 A plane contains at least three noncollinear
points.
• 10 If two points lie in a plane, then the line
connecting them lies in the plane.
• 11 If two planes intersect, then their
intersection is a line.

7
Postulate 5 Through every two points, there is
exactly one line.
• As with all postulates, this should be obvious.
• It lets us use the notation AB to refer to the
line through points A and B. Without this
postulate, we wouldnt know that there is such a
line and there could be more than one.
• Example of more than one
• Look at the North and South poles of a globe.
• If we allow lines to be drawn on the sphere,
there are many lines going from the North Pole to
the South Pole (lines of longitude).
• Since we draw lines on planes instead of spheres,
this does not happen.

8
Postulate 6 Every line contains at least two
points.
• Every line actually contains an INFINITE number
of points.
• This postulate mentions only two because its a
less strict requirement.
• In Math, we try to keep the postulates as
non-restrictive as we can.

9
Postulate 7 If two lines intersect, their
intersection is exactly one point.
• P
• To see why we need this, remember the globe
• Any line going through the north pole would
also go through the south pole.
• These are lines of longitude.
• All such lines would intersect in two points
• We are drawing our lines on planes, so that
cannot happen.

10
Postulate 8 Through any three noncollinear
points, there exists exactly one plane.
• Remember the triangle we created with string the
first week of school? That triangle is part of
• If the three points were collinear, we could have
many planes through them all in fact, an
infinite number.
• This is a lot like Postulate 5 (through any two
points there is exactly one line).

11
Postulate 9 A plane contains at least three
noncollinear points.
• There are actually infinite points were just
trying to be non-restrictive again. (Three is a
weaker requirement).
• The three points form a triangle in the plane.
• This is like Postulate 6 (a line contains at
least two points).

12
Postulate 10 If two points lie in a plane, then
the line connecting them lies in the plane.
• We know that there is such a line because of
Postulate 5.
• This is an example of why Postulate 5 is
important.

13
Postulate 11 If two planes intersect, then
their intersection is a line.
diagram) on the Chapter 1 test.
• Example
• The floor of the classroom intersects with the
front wall of the classroom.
• Their intersection is the line along the bottom
of that wall.

14
Solutions are on the next slide. No peeking!
15
(No Transcript)
16
Solutions are on the next slide.
17
(No Transcript)
18
Diagrams Lie!
• Reminder Diagrams are often misleading. Here
are some examples.

19
Perpendicular Figures
• This is an example of where symbols such as the
red right angle marker are important.
• Without them, we would not be able to assume that
line t really is perpendicular to the plane.

20
A 3-D Diagram
The solution is on the next slide.
21
A 3-D Diagram
• A, B, and F are collinear, since line AF is
shown and B is on it in the diagram.
• E, B, and D are collinear dont have such a
line shown. We cant assume.
• Segment AB is shown with a perpendicular mark,
so we know that it is ? plane S.
• Segment CD doesnt have such a mark we cant
assume that its perpendicular to plane T.
• The diagram clearly shows that lines AF and BC
intersect at point B, so we know that is true.

22
Classwork
• You have a handout with the pages needed for this
assignment.
• Do 3-8, 11-13, 14-23, 26, 29, 31, 32, 39, 42, 45.