Chapter 2 Team Game

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Chapter 2 Team Game

• Work together win the candy.

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Rules

• The teams will be groups of 4 assigned by the
  teacher
• The eldest person in the group is the presenter
  (and only the eldest!)
• Everyone in the group must participate in coming
  up with the answer.
• A question will presented at the beginning to
  decide who gets to pick the category first.
• When a category is picked, a problem will be
  presented for all teams to attempt.
• Once the team decides on an answer, they send the
  presenter up to the desk to present their answer
  (and work!) to the teacher.
• If the work and answer is correct, then the
  presenters team is awarded the points.
• The team to win the game will get their choice of
  the teachers candy!

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Deciding Question

• State whether the statement is true or false. If
  the statement is false, say why.
• If two lines intersect, then their intersection
  is exactly two points.
• False If two lines intersect, then their
  intersection is exactly ONE point.

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Conditional Statements 100

• Write the following statement in If- then form.
• Two points are collinear if they lie on the same
  line
• If two points are collinear, then they lie on the
  same line.

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Conditional Statements 300

• Write a counterexample for the following
  statement
• If a number is odd, then it is divisible by 3.
• Sample answer 7 is odd, but is not divisible by 3

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Conditional Statements 200

• Rewrite in if-then form.
• All mammals breathe oxygen.
• If an animal is a mammal, then it breathes oxygen

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Conditional Statements 400

• Rewrite in if-then form
• All monkeys have tails
• If an animal is a monkey, then it has a tail.

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Conditional Statements 500

• Write a counterexample for the following
  statement
• If a number is divisible by 2, then it is
  divisible by 4.
• Sample answer 14 is divisible by 2, but not by 4

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Conditional Statements 600

• State the following is true or false. If it is
  true, rewrite it in if-then form. If it is false,
  rewrite it so that it is a true statement.
• A plane contains at least two noncollinear
  points.
• False A plane contains at least THREE
  noncollinear points.

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Rewriting Statements 100

• Write the converse of the statement
• If two segments have the same length, then they
  are congruent.
• If two segments are congruent, then they have the
  same length.

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Rewriting Statements 200

• Write the converse of the statement
• If the television is on, the teenager will not
  get their homework done.
• If the teenager will not get their homework done,
  then the television is on.

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Rewriting Statements 300

• Write the inverse of the statement
• If there is snow on the ground, then the flowers
  are not in bloom.
• If there is not snow on the ground, then the
  flowers are in bloom.

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Rewriting Statements 400

• Write the inverse of the statement
• If two planes intersect, then their intersection
  is a line.
• If their intersection is a line, then two planes
  are intersecting.

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Rewriting Statements 500

• Write the contrapositive of the statement
• If two points lie in a plane, then the line
  containing them lies in the plane.
• If the line containing two points does not lie in
  the plane, then they (the two points) do not lie
  in the plane.

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Rewriting Statement 600

• Write the statement in if-then form, then write
  its inverse, converse, and contrapositive.
• A line contains at least two points.
• If there is a line, then it contains at least two
  points.
• Inverse If there is not a line, then it does not
  contain at least two points.
• Converse If it contains at least two points,
  then it is a line.
• Contrapositive If it does not contain at least
  two points, then it not a line.

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Biconditional 100

• What is a biconditional statement?
• A statement with the phrase if and only if in
  it.
• Writing a biconditional statement is equivalent
  to writing a conditional statement AND its
  converse.

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Biconditional 200

• Write the conditional statement as a
  biconditional statement
• If I eat too much candy, then my teeth will fall
  out.
• If and only if I eat too much candy, then my
  teeth will fall out.
• I eat too much candy if and only if my teeth fall
  out.

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Biconditional 300

• Rewrite the biconditional statement as a
  conditional statement and its converse.
• Three lines are coplaner if and only if they lie
  on the same plane.
• CS If three lines are coplanar, then they lie in
  the same plane.
• Converse If three lines lie in the same plane,
  then they are coplanar.

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Biconditional 400

• Determine whether the statement can be combined
  with its converse to form a TRUE biconditional
  statement.
• If v 1, then 9v 4v 2v 3v.
• No, v can be any number if 9v 4v 2v 3v.

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Biconditional 500

• Rewrite the true statement if if-then form and
  write the converse. If the converse is true,
  write it as a biconditional statement. If it is
  false, provide a counterexample.
• All leopards have spots.
• If an animal is a leopard, then it has spots.
• Converse If an animal has spots, then it is a
  leopard.
• False sample answer a Dalmatian has spots

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Biconditional 600

• Give an example of a true biconditional
  statement.
• Sample Answer You received an A or B in all of
  your classes if and only if you made the honor
  roll.

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Symbolic Notation 100

• Identify the p (hypothesis) and the q
  (conclusion) of the statement
• If it is raining, then the soccer game is
  canceled
• p it is raining
• q the soccer game is canceled

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Symbolic Notation 200

• What is the symbolic notation for converse,
  inverse, and contrapositive?
• Converse q ? p
• Inverse p ? q
• Contrapositive q ? p

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Symbolic Notation 300

• Write in words the converse of the statement as
  well as the symbolic notation.
• If you do not finish your dinner, then it will
  not be a sunny day tomorrow.
• Converse If it will not be a sunny day tomorrow,
  then you do not finish your dinner. Symbolic q ?
  p

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Symbolic Notation 400

• State whether the argument is valid through the
  law of detachment or syllogism.
• Jamal knows if he misses practice the day before
  a game, then he will not be a starting player.
• Jamal misses practice on Tuesday so he
  concludes that he will not be able to start in
  the game on Wednesday.
• Valid the law of detachment

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Symbolic Notation 500

• Use the Law of Syllogism to write a conditional
  statement using the following
• If a bird is a bee hummingbird, then it is the
  smallest of all birds.
• If a bird is the smallest bird, then it has a
  nest the size of a walnut half-shell.
• If a bird is a bee hummingbird, then it has a
  nest the size of a walnut half-shell.

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Symbolic Notation 600

• Use the true statements to answer the question
  that follows
• If a creature is a fly, then it has six legs.
• If a creature has six legs, then it is an insect
• Use the Law of Syllogism to write a conditional
  statement, both in words and in symbols.
• p ? r If a creature is a fly, then it is an
  insect

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Proofs 200

• What is the Transitive Property?
• If a b and b c, then a c.

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Proofs 100

• What is the Addition Property?
• If a b, then a c b c

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Proofs 300

• Write the Reflexive Property for both SEGMENT
  LENGTH and ANGLE MEASURE.
• For any segment AB, AB AB
• For any angle A, m?A m?A

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Proofs 400

• Solve the equation and state a reason for each
  step.
• 3(v 1) 8v 17
• 3v 3 8v 17 (Distributive Prop.)
• -5v 3 17 (Simplify / Combine like terms)
• -5v 20 (Addition Prop.)
• V -4 (Division Prop.)

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Proofs 500

• In a two column proof,
• Given
• Prove

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Proofs 600

• In a two column proof
• Given m?3 120, ?1 ? ?4, ?3 ? ?4
• Prove m?1 120

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