Loading presentation...

Present Remotely

Send the link below via email or IM

Copy

Present to your audience

Start remote presentation

  • Invited audience members will follow you as you navigate and present
  • People invited to a presentation do not need a Prezi account
  • This link expires 10 minutes after you close the presentation
  • A maximum of 30 users can follow your presentation
  • Learn more about this feature in our knowledge base article

Do you really want to delete this prezi?

Neither you, nor the coeditors you shared it with will be able to recover it again.

DeleteCancel

Make your likes visible on Facebook?

Connect your Facebook account to Prezi and let your likes appear on your timeline.
You can change this under Settings & Account at any time.

No, thanks

Geometry Chapter 2

No description
by

Mc Senderak

on 16 January 2015

Comments (0)

Please log in to add your comment.

Report abuse

Transcript of Geometry Chapter 2

Come up with a true conjecture and a false conjecture to this statement: Line AB intersects Line CD at point K.
Geometry Chapter 2
Objectives
Conditional Statements
Conjectures
Math History:
Proofs
Geometric proofs date back a very long way. Two Ancient Greek mathematicians named Exodus and Theaetetus drew up theorems but did not prove them. The Greek philosopher Thales proved geometric theorems, however, he didn't use two-column proofs as we do in math class. Finally, a man named Euclid of Alexandria used undefined terms,

which were self-evidently true, and deductive logic to prove theorems true. He transformed proofs with that, and Islamic mathematicians advanced them a little further before the proof theory we use today took shape. Axioms, which are statements that suggest that undefined terms are true, are no longer assumed true, allowing for more mathematical theories to be built.
By: Emily, Micaela, and Reilly
Chapter 2 of Geometry is mainly about reasoning and geometric proofs. This chapter covers topics like conjectures, inductive/deductive reasoning, logic, conditional statements, and algebraic or two-column proofs. Today, we're presenting Chapter 2 in just a few minutes, but given our presentation, we can prove that you'll remember all of the content by the end!


Chapter 2: Reasoning and Proofs

Mathletics
1. If an animal is spotted, then it is a Dalmatian.
Choose the hypothesis of the following statements
2. If today is Thanksgiving, then today is Thursday.
Write each statement in if-then form
3. Cheese contains calcium.
4. The measure of an acute angle is between 0 and 90.
Write the converse, inverse, and contrapositive of each conditional statement.
6. If a triangle is a right triangle, then it has one right angle.
5. If two angles are supplementary, then they each measure 90.
Draw the object that would come next in the following pattern.
7.
Students will review:
Conjectures
Conditional Statements
Law of Detachment and Syllogism
Proofs
Possible answers:
Get a free phone with a two-year service contract.
Equiangular triangles are equilateral.
Answers:
If you get a two-year service contract, then you get a free phone.
If a triangle is equiangular, then it is equilateral.
If p, then q
P is hypothesis
Q is conclusion
Converse (if q, then p)
Inverse (if not p, then not q)
Contrapositive (if not q, then not p)
Biconditional (p if and only if q)
How they Work
C
D
A
B
K
Put the following statements into if-then form.
What is the converse of the statement "Vertical angles are congruent."
Conditional Statements cont.
Conjectures cont.
Educated guess
Can be true or false
False need a counterexample
Conditional Statements cont.
Answer: If angles are congruent, then they are vertical
Different conditionals have different truth values
Show in truth table
Converse and inverse correlate
Conditional and contrapositive correlate
Detachment & Syllogism

1. A midpoint divides a segment into 2 congruent parts

2. C is the midpoint of RS

3. RC is congruent to CS


Which Law?
If p then q is true, and p is true, then q is true
Two variables
Detachment
Laws cont.
True: Angle AKC is congruent to Angle BKD.

False: Line AC is perpendicular to line BD.
Counterexample: m<AKC = 87 degrees
Syllogism

1. If we have over 4 in. of snow, the buses cannot drive.

2. If the buses cannot drive, school will be canceled.

3. ???


Answer: If we have over 4 inches of snow, school will be canceled.

IF p then q is true AND if q then r is true THEN p then r is true.
Must follow the certain order
Wrong Order= NO possible conclusion
Proofs... BREIFLY!
Postulates
and
Theoroms
are used in proofs
Postulates
are accepted
Theoroms
are proven
Properties
are also used
Ex. Addition Prop, Transitive Prop.
Full transcript