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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.

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.

Use Postulates and Diagrams

- Section 2.4

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.

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

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.

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.

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.

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

instead of one! - We are drawing our lines on planes, so that

cannot happen.

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

the plane were talking about. - 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).

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).

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.

Postulate 11 If two planes intersect, then

their intersection is a line.

- There was a question about this (along with a

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.

Solutions are on the next slide. No peeking!

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Solutions are on the next slide.

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Diagrams Lie!

- Reminder Diagrams are often misleading. Here

are some examples.

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.

A 3-D Diagram

The solution is on the next slide.

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.

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.