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Geometry
October 20, 2016
CHAPTER 2 REVIEW
DO NOW
Solve for x. Write all of your steps clearly.
1.
2.
Agenda
• Announcements (2nd hour only)
• Do Now
• Review for Quiz
• Exercises
REMINDER
•Chapter 2 Quiz TOMORROW!
Objective/Big Question
What does it mean to “prove”
something in mathematics?
Exercises from yesterday
Conjecture
• A prediction we make based on a pattern of numbers
• PROVE: Use a formal PROOF to make a conjecture a THEOREM
• DISPROVE: Find a single COUNTEREXAMPLE
Conditional
• An “if-then” statement: Something which states that, if A is true, then
B is true.
If today is Monday, we have to go to school.
If it’s cold outside, you should wear a coat.
If 3x = 12, then x = 4.
Hypothesis
• The “if” statement: What we are saying might be true.
If today is Monday, we have to go to school.
If it’s cold outside, you should wear a coat.
If 3x = 12, then x = 4.
Conclusion
• The “then” statement: What logically follows from the hypothesis.
If today is Monday, we have to go to school.
If it’s cold outside, you should wear a coat.
If 3x = 12, then x = 4.
Euler Diagram
• All whole numbers are integers
• Conditional: If a number is a
whole number, it is an integer.
Biconditional
• If a CONDITIONAL and its CONVERSE are both true, we can write it as
a “biconditional”:
HYPOTHESIS if and only if CONCLUSION
• A number is prime if and only if it is greater than one and
has no factors other than itself and one.
• 5x = 20 if and only if x = 4
Definition
• A DEFINITION is a BICONDITIONAL with a vocabulary word as its
HYPOTHESIS:
• A number is prime if and only if it is greater than one and
has no factors other than itself and one.
• An angle is right if and only if its measure is 90°.
Proofs
• Given: What you’re told is true
• Prove: What you intend to show, using the given information and
known properties, postulates, and theorems
• Two-column proof: Each step of your proof is provided, with a stated
reason for each step, in a table
• Paragraph proof: Same steps, written as a paragraph
Key Properties
• REFLEXIVE PROPERTY: Everything is congruent to itself
• SYMMETRIC PROPERTY: You can “flip” equalities and congruencies
• TRANSITIVE PROPERTY: If two things are both congruent to a third
thing, they’re congruent to each other
• SUBSTITUTION: If two values are equal, you can swap them out
Vertical Angles Theorem
• VERTICAL ANGLES are always congruent
• ∠1 ≅ ∠3
𝑚∠1 + 𝑚∠2 = 180°
Quiz Review