070912 Biconditionals and Definitions
Write the converse of this conditional and determine the truth value of each.
If two lines intersect to
from right angles, then they are perpendicular.
When a conditional and itÕs
converse are both true, both statements can be combined to form what is called
a ÔBiconditionalÕ. What does this
mean? A biconditional, in a
nutshell, says that for one to be true, the other must be true and vice versa.
The two statements above can be written as:
Two lines intersect to form
right angles if and only if they are perpendicular.
Can you write this statement
in reverse order and still have the same meaning?:
How about this statement:
X^2 = 100 if and only if x =
10.
Is this statement a Ôtrue
biconditionalÕ?
Now what about definitions?
Here is a definition of
ÔbookÕ
book: A book is something that you read.,
Is this a good
definition?
What properties can make a
good definition?
How about some of the
definitions we have in our Book of Knowledge? Here are some terms we have defined during the past 4
weeks. For each term, write
itÕs definition from the Book of Knowledge, and answer the questions that
follow.
Distance from a point to a
line:
a. Are the words we used easily understandable?
b. Is the definition precise?
c. Write the definition as a biconditional. (Hint: First write the statement as a conditional, then itÕs
converse. Determine the truth
value of each, and write the biconditional)
Equidistant Point:
a. Are the words we used easily understandable?
b. Is the definition precise?
c. Write the definition as a biconditional.
Midpoint:
a. Are the
words we used easily understandable?
b. Is the definition precise?
c. Write the definition as a biconditional.
Segment Bisector:
a. Are the words we used easily understandable?
b. Is the definition precise?
c. Write the definition as a biconditional.
Perpendicular Bisector:
a. Are the words we used easily understandable?
b. Is the definition precise?
c. Write the definition as a biconditional.
Circle:
a. Are the words we used easily understandable?
b. Is the definition precise?
c. Write the definition as a biconditional.
Angle Bisector:
a. Are the words we used easily understandable?
b. Is the definition precise?
c. Write the definition as a biconditional.