8. Elements
this is the
book of Euclid
which contains
the
fundamentals
and concepts
in Geometry.
9. Thoughts to ponder:
What do you think will happen if
Geometry was not discovered or
introduced to the World?
•What would its effects to the
infrastructure? to houses? to
businesses?
27. For BICONDITIONAL:
CONVERSE: If an animal has
mammary gland, then it is a
mammal. (TRUE)
BICONDITIONAL: An animal
is a mammal if and only if it
has a mammary gland. (TRUE)
28. Conditional statement
may be true or false. To show
that a conditional statement
is TRUE, you must construct
a logical argument using
reasons.
29. 1. Definition- a statement of
a word, or term, or phrase
which made use of
previously defined terms
2. Postulate- is a statement
which is accepted as true
without proof.
30. 3. Theorem- is any statement
that can be proved true.
4. Corollary- to a theorem is a
theorem that follows easily
from a previously proved
theorem.
31. EXAMPLE 2:
Complementary angles are any two
angles whose sum of their measure
is 90.
CONDITIONAL: If two angles
are complementary, then the
sum of their measure is 90 .
TRUE
32. CONVERSE: If the sum of the
measures of two angles is 90,
then they are
complementary. TRUE
BICONDITIONAL: Two angles
are complementary if and
only if the sum of their
measure is 90. TRUE
33. INVERSE: If two angles are
not complementary, then the
sum is not . TRUE
CONTRAPOSITIVE: If the
sum of the measures of two
angles is not 90, then they are
not complementary. TRUE
34. EXAMPLE 3:
The sum of two odd numbers is
even.
CONDITIONAL: If two
numbers are odd, then their
sum is even. TRUE
CONVERSE: If the sum of two
numbers is even, then they
are odd numbers. TRUE
35. BICONDITIONAL: Two
numbers are odd if and only
if their sum is even. TRUE
INVERSE: If two numbers are
even, then their sum is odd.
FALSE
37. DEDUCTIVE REASONING
-from deduce means to reason
form known facts;
-use in proving theorem;
-using existing structures to
deduce new parts of the
structure.
-“if a, then b”
38. SYLLOGISM
- an argument made up of three
statements: a major premise, a
minor premise (both of which
are accepted as true), and a
conclusion.
39. EXAMPLES OF SYLLOGISM:
Major Premise: If the
numbers are odd, then their
sum is even.
Minor Premise: The numbers
3 and 5 are odd numbers.
Conclusion: the sum of 3 and
5 is even.
40. EXAMPLES OF SYLLOGISM:
Major Premise: If you want
good health, then you should
get 8 hours of sleep a day.
Minor Premise: Aaron wants
good health.
Conclusion: Aaron should get
8 hours of sleep a day.
41. EXAMPLES OF SYLLOGISM:
Major Premise: Right angles
are congruent.
Minor Premise: ∟1 and ∟2
are right angles.
Conclusion: ∟1 and ∟2 are
congruent.
42. EXAMPLES OF SYLLOGISM:
Major Premise: Diligent
students do their homeworks.
Minor Premise: Amy and
Andy are diligent students.
Conclusion: Amy and Andy do
their homeworks.
43. INDUCTIVE REASONING:
It is a process of observing
data, recognizing patterns,
and making generalizations
from observations.
44. Geometry is rooted in
inductive reasoning. The
geometry of ancient times
was a collection of
procedures and
measurements that gave
answers to practical
problems.
45. Used to calculate land areas,
build canals, and build
pyramids.
Using inductive reasoning to
make a generalization called
conjecture.