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GEOMETRY
VOCABULARY
TOOLKIT
CONDITIONAL STATEMENT


IF P THEN Q
If today is Wednesday then tomorrow is
Thursday.
INVERSE
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
IF NOT P THEN NOT Q
If today is not Wednesday then tomorrow
is not Thursday.
CONVERSE
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
IF Q THEN P
If tomorrow is Thursday then today is
Wednesday.
CONTRAPOSITIVE


IF NOT Q THEN NOT P.
If tomorrow is not Thursday then today is
not Wednesday.
BICONDITIONAL
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


YOU HAVE A BICONDITIONAL IF THE
CONDITIONAL AND THE CONVERSE
ARE BOTH TRUE.
If today is Wednesday, then tomorrow is
Thursday. (true)
If tomorrow is Thursday, then today is
Wednesday. (true)
Biconditional: Today is Wednesday if and
only if tomorrow is Thursday.
LOGICAL CHAIN


A LOGICAL SEQUENCE OF EVENTS
Example:
If it rains I am going shopping.
If I go shopping I will purchase an
umbrella.
If I purchase an umbrella I won’t get wet.
Therefore, if it rains I won’t get wet.
CONJECTURE


AN EDUCATED GUESS
Example:
If I do not study I will not pass the test.
COUNTEREXAMPLE


AN EXAMPLE THAT DISPROVES A
CONDITIONAL STATEMENT.
Example:
If the animal is a mammal then it is a dog.
Counterexample: cat
HYPOTHESIS


PART OF A CONDITIONAL STATEMENT
THAT FOLLOWS THE “IF”
Example:
If today is Wednesday then tomorrow is
Thursday
CONCLUSION


THE PART OF A CONDITIONAL
STATEMENT THAT FOLLOWS “THEN”
Example:
If today is Wednesday then tomorrow is
Thursday
REFLEXIVE PROPERTY

A=A

Example:
In the figure below AL = AL
SYMMETRIC PROPERTY


IF A = B, THEN B = A
Example:
If x = 3 then 3 = x
TRANSITIVE PROPERTY

IF A = B AND B = C, THEN A = C.

Example:
If m1 = m2 and m2 = m3 then,
m1 = m3
POSTULATE


ASSUMED TO BE TRUE
Example:
If point B is between points A and C on a
line then AB + BC = AC (Segment Addition
Postulate)
ANGLE ADDITION
POSTULATE


The sum of the measures of two adjacent
angles is equal to the measure of the angle
formed by the two outside rays.
Example: m1 + m2 = mABC
SEGMENT ADDITION
POSTULATE

IF POINT Q IS BETWEEN POINTS P
AND R ON A LINE, THEN
PQ + QR = PR
Example:
COMPLEMENTARY ANGLES


A PAIR OF ANGLES WITH MEASURES
TOTALING 90°
Example: (Angles do not have to be
adjacent)
SUPPLEMENTARY ANGLES


A PAIR OF ANGLES WITH MEASURES
TOTALING 180°
Example:
Angles 1 and 2 are supplementary (Note:
they do not have to be adjacent)
LINEAR PAIR



TWO ANGLES FORMED WHEN A RAY IS
DRAWN FROM A POINT ON A LINE.
THE ANGLES ARE ADJACENT AND
SUPPLEMENTARY.
Example:
VERTICAL ANGLES



ANGLES FORMED BY THE
INTERSECTION OF TWO LINES.
ANGLES OPPOSITE EACH OTHER ARE
CONGRUENT.
Example: m1 = m3
m4 = m2