MATH TIPS

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MATH TIPS
for PARENTS
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NUMBER PROPERTIESTHE OPERATION CALLED ADDITION
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Associative Property of Addition

• Changing the grouping of the terms (addends) will
  not change the sum (answer in addition).
• In Arithmetic (5 3) 2 5 (3 2) In
  Algebra (a b) c a (b c)

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Commutative Property of Addition

• Changing the order of the numbers (addends) will
  not change the sum (answer in addition). In
  Arithmetic 8 4 4 8 In Algebra a b
  b a

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Identity Property of Addition

• Zero added to any given number (given
  addend), the sum will equal the given number
  (given addend).
• In Arithmetic 6 0 6 In Algebra a 0
  a

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Inverse Operation of Addition

• Subtraction undoes the operation called
  addition. In Arithmetic If 7 4 11,
  then 11 - 7 4 and 11 - 4 7 In
  Algebra a b c, then c - a b and c -
  b a

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THE OPERATION CALLED SUBTRACTION
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Inverse Operation of Subtraction

• Addition undoes the operation called
  subtraction. In Arithmetic If 16 - 9 7,
  then 9 7 16 and 7 9 16 In
  Algebra c - b a, then b a c and a
  b c

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THE OPERATION CALLED DIVISION
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Inverse Operation of Division

• Multiplication undoes the operation called
  division. In Arithmetic If 48 / 8 6,
  then 8 x 6 48 and 6 x 8 48 In
  Algebra c / b a, then b x a c and a x
  b c

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THE OPERATION CALLED MULTIPLICATION
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Associative Property of Multiplication

• Changing the grouping of the factors will not
  change the product (answer in multiplication). I
  n Arithmetic (5 x 4) x 2 5 x (4 x 2) In
  Algebra (a x b) x c a x (b x c) or (ab) c
  a (bc)

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Commutative Property of Multiplication

• Changing the order of the factors (multiplicand
  and multiplier) will not change the product
  (answer in multiplication). In Arithmetic 6 x
  9 9 x 6 In Algebra a x b b x a or ab
  ba

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Identity Property of Multiplication
Identity Property of Multiplication

• The product (answer in multiplication) and 1 is
  the original number. In Arithmetic 7 x 1
  7 In Algebra a x 1 a or a 1 a

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Multiplication Property of Zero

• The product (answer in multiplication) of any
  number and zero is zero. In Arithmetic 9 x 0
  0 In Algebra a x 0 0 or a 0 0
  Multiplication is repeated
  addition. 8 x 4
  8 8 8 8

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Distributive Property of Multiplicationover
Addition or Subtraction
Distributive Property of Multiplicationover
Addition or Subtraction

• Multiplication by the same factor may be
  distributed over two or more addends. This
  property allows you to multiply each term inside
  a set of parentheses by a term inside the
  parentheses. In many cases this is an excellent
  vehicle for mental math. In Arithmetic OVER
  ADDITION 5(90 10) (5 x 90) (5 x
  10) OVER SUBTRACTION 5(90 - 10) (5 x 90)
  - (5 x 10) In Algebra OVER ADDITION a(b
  c) (a x b) (a x c) or a(b c) ab
  ac OVER SUBTRACTION a(b - c) (a x b) -
  (a x c)

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GLOSSARY ofMATHEMATICAL TERMS
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Add/Addend/Addition/Array
ADDTo put one thing, set or group with another
thing, set or group. ADDENDNumbers to be
added. Example 12 23 25 a b c
abc ADDITIONThe operation of putting together
two or more numbers, things, groups or
sets. Example 8 2 4 14 is an addition
problem ARRAYAn orderly arrangement of persons
or things, rows and columns. The number of
elements in an array can be found by multiplying
the number of rows by the number of
columns. Example
3 x 6 18
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Associative Property of Addition-Multiplication/At
tribute
ASSOCIATIVE PROPERTY OF ADDITIONThe way in which
three numbers to be added are grouped two at a
time does not affect the sum. Example 3 (5
6) (3 5) 6 3 11 8 6
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14 ASSOCIATIVE PROPERTY OF MULTIPLICATIONThe way
in which three numbers to be multiplied are
grouped two at a time does not affect the
product. Example 3 x (2 x 6) (3 x 2) x 6
3 x 12 6 x 6
36 36 ATTRIBUTEA quality
that is thought of as belonging to a person of
thing. Characteristics such as, size, shape,
color and/or thickness.
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Average/Axis
AVERAGEA number found by dividing the sum
(total) of two or the sum (total) of two or more
quantities by the number of quantities. The
average of 86, 54, 9 and 93 is 68. STEP
1 STEP 2 86 68 is the
average 54 How many addends? 4)
272 39 Quantity is 4 -
24 93 32 272 sum or total
- 32 0 AXIS
(axes)Horizontal and vertical number lines in a
number plane.
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Bar Graph/Braces
Colors the Class Likes
BAR GRAPHA picture in which number
informationis shown by means of bars of
different lengths. BRACESBraces are symbols
. They are used to list names of numbers
(elements) of a set. Example Pauline, April,
Joni, Jackie is a set of secretaries. Sund
ay, Monday, Tuesday, Wednesday, Thursday,
Friday, Saturday is a set of the days of the
week. 1, 2, 3, 4, 5, 6, 7, 8, 9 is a set of
counting numbers from 1 to 9.
25 20 15 10 0
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Capacity/Cardinal Number/Centigrade/Cent/Centimete
r
CAPACITYThe amount that can be held in a
space. CARDINAL NUMBERA number that tells how
many there are. Example
There are five squares CENTIGRADEDivided into
one hundred degrees (100). On the centigrade
temperature scale, freezing point is at zero
degrees (0). The boiling point water is at one
hundred degrees (100º) Celsius scale is the
official name of the temperature CENTA coin of
the United States and Canada. One hundred cents
make a dollar. CENTIMETERA unit of length in the
metric system. A centimeter is equal to one
hundredths of a meter or .39 of an inch.
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Century/Closed Figure/Closure
CENTURYA period of one hundred years. CLOSED
FIGUREA geometric figure that entirely encloses
part of the plane. CLOSUREA property of a set of
numbers such that the operation with two or more
numbers of that set results in a number of the
set. Example In addition and multiplication
with counting numbers, the results is a
counting numbers. 2 4 6 2 x 4 8
Thus, the counting numbers are closed under
these two operations. In subtraction, if
4 is subtracted from 2, the result (-2) is
not a counting number. Also in dividing a
2 by 4, the results (1/2) is not a counting
number. Thus, the counting numbers are not
closed with respect to subtraction and division.
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Combine/Common/Common Factor/Common Multiple
COMBINETo put (join) together. COMMONBelonging
equally to all. COMMON FACTORA common factor of
two or more numbers is a number which is a factor
of each of the numbers.Example 8 1, 2,
4, 8 32 1, 2, 4, 8, 16, 32 1, 2,
4 and 8 are the common factors of 8 and 32 COMMON
MULTIPLEA common multiple of two or more numbers
is a number which is a multiple of each of the
numbers.Example 12 12, 24, 36, 48, 72,
84, 96, 108, 120 15 15, 30, 45, 60,
75, 90, 105, 120, 135, 150 60 and 120 are
the common multiples
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Commutative Property of (Addition)(Multiplication)
/Compare/Composite Number
COMMUTATIVE PROPERTY OF ADDITIONThe order of two
numbers (addends) may be switched around and the
answer (total, sum) is the same. Example 7 4
11 and 4 7 11 therefore, 7 4 4
7 COMMUTATIVE PROPERTY OF MULTIPLICATIONThe
order of two numbers (factors) may be switched
around and the answer (total product) is the
same. Example 8 x 6 48 and 8 x 6 48
therefore, 8 x 6 6 x 8 COMPARETo study,
discover and/or find out how persons or things
are alike or different. COMPOSITE NUMBERA
number which has factors other than itself and
one.Since 16 1 x 16, 2 x 8 and 4 x 4, it is a
composite number.
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Conditional Sentence/Congruent Figure/Conjecture/C
onjunction
CONDITIONAL SENTENCE (In logically thinking)A
sentence of the form if. . ., then. .
.? Example If 6 x 7 42 and 7 x 6 42,
Then 42 - 6 7 and 42 - 6 7 CONGRUENT
FIGUREGeometric shapes consisting of the same
shape and size. Example 8 x 6 48 and 8 x 6
48 therefore, 8 x 6 6 x 8 CONJECTUREA
guess resulting from an experiment. Example 2,
4, 6, 8, 10 are even numbers therefore, even
numbers must have 0, 2, 4, 5, or 8 in the
ones place. CONJUNCTION (In logically
thinking)A two-part sentence joined by and to
form true parts. Example 1/4 1/4 2/4 1/2
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Coordinates/Counting Number/Decade/Decimal
COORDINATESTo numbers, an ordered pair, used to
plot a point in a number plane. COUNTING NUMBER
(Natural Numbers)To numbers, an ordered pair,
used to plot a point in a number
plane. Example 1, 2, 3, 4, 5. . . There is
no longest number. Counting numbers are
infinite. DECADEA period of ten
years. DECIMALNames the same number as a
fraction when the denominator is 10, 100, 1000. .
. It is written with a decimal
point. Example .75
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Decimal System/Diagonal/Degree/Denominator
DECIMAL SYSTEMA plan for naming numbers that is
based on ten is called a decimal system of
numeration. The Hindu-Arabic system is a decimal
system. DIAGONALA straight line that connects
the opposite corners of a rectangle. Example
DEGREEA unit of angle measurement. DENOMINATORIn
3/5 the denominator is 5. It tells the number
of equal parts, groups or sets the whole was
divided.
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Difference/Digit/Disjoint Sets
DIFFERENCEThe number which results when one
number is subtracted from another is called the
difference. It is a missing addend in
addition. Example 7 - 4 3 the difference
is 3 DIGITAny one of the basic numerals, 0, 1,
2, 3, 4, 5, 6, 7, 8, 9, is a digit.The numeral
12 is a two-digit numeral and the numeral 354 is
a three digit numeral. DISJOINT SETSSets that
have no members in common are disjoint
sets. Example Set A a, b, Set B 1, 2,
3. Sets A and B are disjoint
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Distributive Property of Multiplication over
Addition/Divide/Dividend
DISTRIBUTIVE PROPERTY OFMULTIPLICATION OVER
ADDITIONMultiplication by the same factor may be
distributed over two or more addends. Example 3
x (6 4) (3 x 6) (3 x 4)
18 12 30 DIVIDETo separate
into equal parts, pieces, groups or
sets.. Example x x x x x x x x x
x 10 ? 2 5 DIVIDENDA number that shows the
total amount to be separated into equal parts,
groups of sets by another number. Example 100 ?
25 4, the dividend is 100
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Divisible/Divisor/Element/Element of a Set/Empty
Set
DIVISIBLECapability of being separated equally
without a remainder. Example 18 is divisible by
1, 2, 3, 6, 9 and 18 DIVISORA number that tells
what kind of equal parts, groups or sets the
dividend is to be separated. ELEMENTA member of
a set. ELEMENT OF A SETA member of a
set. EMPTY SETThe set which has no members.
The number of the empty set is zero. A symbol
for the empty set is .
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Equal/Endpoint/Equal Sets/Equal Sign
EQUALA relationship between two expressions
denoting exactly the same or equivalent
quantities. Example The two expressions 2 6
and 3 5 are said to be equal because they
both denote exactly the same
quantity. ENDPOINTA point at the end of a line
segment or ray. EQUAL SETSTwo sets with exactly
the same things, elements or members. Example A
1, 2, 3 and B 3, 2, 1 EQUAL SIGNThe
equal sign shows that two numerals or expressions
name the same number. Example 10 9 19In a
true sentence, the equal sign shows that the
numerals on each side of the sign name the same
number.
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Equation/Equivalent Sets/Estimate
EQUATIONA number sentence in which the equal
sign is used in an equation. Example 6
10 and 8 - 3 are equations EQUIVALENT
SETSIf the members of two sets can be matched
one to one, the sets are equivalent. Equivalent
sets have the same number of members/elements. EST
IMATEAn estimate is an approximate answer found
by rounding numbers. Example 22 39 ,
22 may be rounded to 20, 39 may be rounded
to 40. The estimated sum is 20 40 or 60
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Even Number/Expanded Numeral/Exponent
EVEN NUMBERAn integer that is divisible by 2
without a remainder. Example 0, 2, 4, 6. . .
Are even numbers EXPANDED NUMERALAn expanded
numeral is a name for a number which shows the
value of the digits. Example An expanded number
for 35 is 30 5 or ( 3 x 10) (5 x
1) EXPONENTA number which tells how many times a
base number issued as a factor. In the example
below the base numbers are 10, 3, and
9. Example 10? 10 x 10 3? 3 x
3 x 3 10? 10 x 10 x 10 x 10 x 10 x 10
9? 9 x 9 x 9 x 9
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Factors/Factor Tree/Fahrenheit
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Fraction-Fractional Numbers/Greater
Than/Greatest Common Factor
FRACTION FRACTIONAL NUMBEREqual parts of a whole
thing, group or set. A number named by a numeral
such as 1/2, 2/3, 6/2, 8/4. GREATER THANLarger
than or bigger than something else. In greater
than the symbol gt, means that the number named at
the left is greater than the number named at the
right. Example 8 gt 3 is a true
sentence GREATEST COMMON FACTORThe greatest
common factor (GCF) of two or more counting
numbers is the largest counting which is a factor
of each of the counting numbers. Example 10
1, 2, 5 12 1, 2, 3, 4, 6, 12 2 is
the G.C.F. for 10 and 12
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Graph
GRAPHA graph shows two sets of related
information by the use of pictures, bars, lines
or a circle. Graphs may be constructed using
horizontal or vertical positions. BOYS
PERFECT ATTENDANCE
TEMPERATURE RECORD Month Girls Present 20 April
10 May June 0 Each symbol
represents 3 girls 10 11
12 1 2 3 Graphs continued on
next page
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Graph/Hindu Arabic Numeration System
GRAPHS (continued) 10,000 9,000 8,000
7,000 6,000 5,000 4,000 3,000
2,000 1,000 0 Caribbean Red
North Japan HINDU ARABIC NUMERATION
SYSTEM(Base Ten Decimal Numeration System)There
are 10 digits namely, 0, 1, 2, 3, 4, 5, 6, 7, 8
and 9. All whole numbers may be represented by
using the digits and Base Ten place value (one,
tens, hundreds. . .) Example 96,5200 (9 x
10,000) (6 x 1,000) (5 x 100) (2
x 10) (0 x 1) or (9 x 10?)
(6 x 10?) (5 x 10?) (2 x 10) (0
x 1)
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Horizontal/Identity Element of (Addition)(Multipli
cation)/Inequality/Integer
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Intersection of Sets/Joining Sets/Kilometer
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Least Common Multiple/Length
LEAST COMMON MULTIPLEThe least common multiple
of two or more counting numbers is the smallest
counting numbers which is a multiple of each of
the counting numbers.Example What are some
multiples of both 4 and 6? Set of
multiples of 4 4, 8, 12, 16, 20, 24, 28, 32,.
. . Set of multiples of 6 6, 12, 18,
24, 30, 36,. . . 12 is multiple of both 4 and 6.
Another multiple of both 4 and 6 is 24.
Therefore, 12 and 24 are called common multiples
of 4 and 6. 12 is the Least Common Multiple
(LCM). LENGTHThe distance from one end to the
other end. Long represents how long something is
from the beginning to the end. Endpoint to
endpoint.
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Less Than/Lowest Terms/Measure/Measure of a Set
LESS THANSmaller than something else. In less
than the symbol lt means that the number to the
left of the symbol is smaller than the number to
the right of the symbol. Example 104 lt 140 5
6 lt 6 6 1/6 lt 1/4 LOWEST TERMSA
fraction is in the lowest or simplest form if the
numerator and denominator have no other common
factors besides 1. Example The lowest terms of
8/32 is 1/4 MEASURETo find or show the size,
weight or amount of something. MEASURE OF A
SETEach thing belonging to a set is a member of
the set. It is also called an element of the
set. Example In a set, A R, S, T, R, S,
and T are members/elements of set A.
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Meter/Metric System/Minuend/Minus
METERThe basic unit of measure is the metric
system. The meter is about 39 inches
long. METRIC SYSTEMA decimal system used for
practically all scientific measurement. The
standard unit of length is the meter. MINUENDThe
number of things, members or elements in all
(whole set) before subtracting. Example 904 is
the minuend of 904 - 756 148 The number from
which another number is taken away
(subtracted). MINUSDecreased by. Lower or less
than. Example 12 - 5 7 The numeral 12 is
decreased by 5 or minus 5.
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Mixed Numeral/Multiple/Multiplicand/Multiplication
MIXED NUMERALA numeral which consists of
numerals for a whole number and a fractional
number. Example 3? MULTIPLE A number that is
multiplied a certain number of times. Example Mu
ltiples of 10 are 10, 20, 30, 40, 50. .
. Multiples of 3 are 6, 9, 12, 15, 18. .
. MULTIPLICAND A number that is to be multiplied
by another number. Example 36 x 14, 36 is the
multiplicand MULTIPLICATIONThe operation of
taking a number and adding it to itself a certain
number of times. Example 4 x 3 4 4
4 25 x 6 25 25 25 25 25 25
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Multiplier/Multiply/Natural Numbers/Negative
Numbers/Number Sentence
MULTIPLIERA number that tells how many times to
multiply another Example 7 x 4 means that 7
will be multiplied 4 times. MULTIPLYTo add a
number to itself a certain number of times.
Shortcut to addition. NATURAL NUMBERSCounting
numbers. NEGATIVE NUMBERSNumbers less than
0. Example -5, -6, -7, -4, -3, -2. . . NUMBER
SENTENCEA sentence of numerical
relationship. Example 2 5 1 6 3 8
gt 6 1 x 3 lt 9 - 2
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Numeral/Numeration/Numerator
NUMERALA symbol for a number. Example The
number word six may be denoted by the symbol
6 thus, 6 is a numeral. NOTE The fundamental
operations(addition, subtraction, multiplication
, division) are performed with numbers, not
with numerals. The word numeral is used only
when referring to the whether to use the word
number or numeral, use the word NUMERATION
A system to name numbers in various
ways. NUMERATOR In 3/5, the numerator is 3. The
numerator tells the number of equal parts, groups
or sets that is being used.
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Odd Number/One-to-One Correspondence
ODD NUMBERAn integer which is divisible by 2
with a remainder. Example ??/??/??/? ONE-TO-ONE
CORRESPONDENCE A one -to-one matching
relationship. If to every member in one set
there corresponds one and only one member in a
second set, and to every member in the second set
there corresponds one and only member in the
first set, the sets are said to be in one-to-one
correspondence. Example If every seat in a room
is occupied by a person, and no person is
standing, there is a one-to-one correspondence
between the number of persons and the
number of seats.
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Open Sentence/Operation/Order
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Ordinal Number/Pair/Per/Percent
ORDINAL NUMBERA number which indicates the order
place of a member of a set in relation to other
members of the same set. Example 1st, 2nd,
3rd. . . PAIR Two persons, animals, or things
that are alike/ that go together. Example A
pair of gloves PER For each. Similar and are
matched to go together. Example eggs per
dozen PERCENTRatio with 100 as its second
number. Percent means per hundred. Example
/100
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Picture Graph/Place Value/Prime Number
PICTURE GRAPHA graph which uses picture symbols
to show number information. Example The
pictograph shows how much money 4 children
earned last week. Each ? means 10
cent. Cierra ? ? ? Alex ? ? ? ?
? ? Paul ? ? ? ? ? Calin ? ?
? ? PLACE VALUE Place value is the value of
each place in a plan for naming numbers. The
value of the first place on the right, in our
system of naming whole numbers is one. The value
of the place to the left of ones place is then. .
. Tens/Ones PRIME NUMBER A number greater than
one which has factors of only itself and one. 2,
3, 5, 7, 11 and 13 are just a few of the prime
numbers.
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Product/Product Set/Quotient/Related Sentences or
Equations
PRODUCTThe number that results when two or more
numbers are multiplied. The answer in a
multiplication problem. Example 2 x 3 6,
the product is 6 PRODUCT SET The set of all
couples formed by pairing every member of one set
with every member of a second set. QUOTIENT In 6
- 2 3, 3 is the quotient. For 13 ? 2, 13 2
x 6 16 is the quotient and 1 is the
remainder. RELATED SENTENCES OR EQUATIONSRelated
sentences give the same number relation in
different ways. Example 4 3 7, 3 4 7,
7 - 4 3, 7 - 3 4 are all related
sentences
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Remainder/Scale Drawing
REMAINDERThe difference of the dividend and the
greatest multiple of the divisor which is less
than the dividend. Example 17 (3 x 5) 2, 3
) 17 The remainder is 2 The part thats
left over. (xxx) (xxx) (xxx) xx
remainder 3 Remainder 2 3
)11 - 9 2 SCALE DRAWING A
drawing the same shape as an object, but which
may be larger, the same size, or smaller than the
object.
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Score/Set/Simplest Forms of a Fractional
Numeral/Standard/Statistics
SCOREA period of twenty years. SET A set is a
collection or group of objects which may be
physical things, points, numbers, and so
on. SIMPLEST FORMS OF A FRACTIONAL NUMERAL In
simplest form, the greatest common factor of the
numerator and the denominator is
one. STANDARDAnything used to set an example or
serve as something to be copied. STATISTICSCollec
tion data expressed through numerical facts.
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Subtract/Subtraction/Subtrahend/Sum
SUBTRACTTo take away from the whole group or
set. Example Take Away ?? ? ? ? ? 5 subtract
2 3 SUBTRACTION The act of taking away some
things, members or elements in the whole group or
set. Example 202 - 197 problem SUBTRAHEND
The number of things, members or elements in the
whole group or set. SUMThe number that results
when two or more numbers are added is the
sum. Example 3 2 5, the sum is 5
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Symbol/Total/Variable
SYMBOLA letter, numeral or mark which represents
quantities, number, operations, or
relations. Example , -, x, ? are symbols for
operations , lt, gt are symbols for
relations The symbol (numeral), 67, may be
used to represent the number word,
sixty-seven. TOTAL The whole amount. VARIABLE
A letter or symbol that represents a number.
The unknown. Example N x 20 100 -
8 5
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Vertical/Weigh/Weight/Whole Numbers/Width
VERTICALStraight up and down. Example 567 49
3 48 WEIGH To measure the heaviness of a
person or thing. WEIGHT The amount of heaviness
of a person or thing. WHOLE NUMBERSThe numbers
which tell how many are whole numbers. The set
of whole numbers contains the counting numbers
and zero. Set of Whole Numbers 0, 1, 2, 3, 4,
5, 6, 7, 8, 9. . . They are infinite. WIDTH
The distance from one side of something to the
other side. How wide something is from one side
to the other side.
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GEOMETRY
Our environment contains many physical objects
for which mathematicians have developed geometric
ideas. These objects then serve as models of the
geometric ideas.
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Common Geometric Symbols
TO NAME A LINE. Illustration AB MEANS
LINE AB. TO NAME A LINE SEGMENT Illustration
AB MEANS LINE SEGMENT AB TO NAME A RAY
Illustration AB MEANS RAY AB. FOR ANGLE
Illustration ABC FOR CONGRUENT
Illustration A B C
D AB CD FOR
TRIANGLE Illustration ABC FOR
PARALLEL Illustration A
B C D
AB CD FOR INTERSECTION
Illustration
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Glossary of Geometric Terms
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Adjacent/Alphabet/Angle
ADJACENTNear or close to something
adjoining. ALPHABETLetters to name geometric
ideas. ANGLEA model to indicate that a line
extends indefinitely in both directions.Illustrat
ion
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Area/Area of a Rectangle
AREA The amount of space enclosed by a plane
figure (simple closed figure). The measure of
the interior (region) of a simple closed figure.
NOTE The measure of the interior of a simple
closed figure is called its area-measure. The
measure of a region is expressed by such terms
as square inches, square centimeters,
square feet, square yard, square meter, etc.
The area of a square one inch long and one inch
wide is a square inch. The area of a square
one foot long and one foot wide is a square
foot. The area of a square one yard long and
one yard wide is a square yard. The area of a
square one meter long and one meter wide is a
square meter. AREA OF A RECTANGLE The number
of square inches in a rectangle equals the number
of rows one inch wide times the number of
square inches in a row.Illustration The
number of square centimeters or square feet in a
rectangle is its area.
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Finding the area of (square)(rectangle)(triangle)(
parallelogram)
TO FIND THE AREA OF A SQUARE Area Side
Squared or A S x S or A S? TO FIND
THE AREA OF A RECTANGLE Area Length times
width (formula) or A L x W or A
LW TO FIND THE AREA OF A TRIANGLE Area
One-half the base times the height or
A ? bh or A TO FIND THE AREA OF A
PARALLELOGRAM Area Base times height over two
plus base times height over two or A
or A 2 or A bh
bh2
bh2
bh2
(bh)2
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Arrow/Bisect/Common/Congruent/Constructions/Curves
ARROWA model to indicate that a line extends
indefinitely in both directions. BISECTSeparate
into two congruent parts. COMMONThe
same. CONGRUENTFigures, in geometry, that have
the same size and shape. CONSTRUCTIONSGeometric
drawings made with only a compass and a straight
edge. CURVESA line having no straight part
bend having no angular part.
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Degree/Diagonal/Dimension/Edge/Enclose
DEGREEA standard unit of measure used in the
measurement of angles. DIAGONALIn a polygon, a
line segment that joins two non-adjacent
vertices extending slantingly between opposite
corners. Illustration DIMENSIONThe
measurement of the length and width. EDGEA line
segment formed by the intersection of two faces
of a solid figure such as a prism. ENCLOSEShut
in all around surrounded.
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Endpoint/Face/Geometric Figure/Geometry/Intersecti
on
ENDPOINTIn a line segment, the two points at the
end of the segment used to name it. FACEA
plane surface of a space figure. GEOMETRIC
FIGUREEvery set of points in space. GEOMETRYThe
study of space and figures in space. INTERSECTIO
NA set that contains all the members common to
two other sets no other members. The
intersection of the model.Illustration
The intersection of angles AYD and CYD is Y.
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Line/Line Segment or Segment
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Line of Symmetry/Midpoint of a Line
LINE OF SYMMETRY A line which divides a figure
into two congruent parts. When a figure is
folded along a line symmetry, the parts fit
exactly on one another. Illustration M
IDPOINT ON A LINE The point on a line segment
which is the same distance from the endpoints
midway between the endpoints of a line
segment. Illustration
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Point Symmetry/Parallel Lines
POINT SYMMETRY Can be fitted onto itself by
making 1/2 turn about a point. Illustration
PARALLEL LINES Two lines in the same plane
that do not intersect. Illustration
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Perpendicular/Parallel
PERPENDICULAR BISECTOR A line which bisects
a segment and is perpendicular to it.
Illustration PARALLELTravel the same
direction apart of every point, so as never to
meet, as lines, planes, etc.
70
Perimeter
PERIMETER The distance around a figure
(polygon). The perimeter of any polygon can be
found by adding the measures of the sides of
the polygon, if they are given in the same
unit. When you find the perimeter of a figure,
the length and the width must be in the same
units. 1. If the dimensions of a figure are
in inches, the perimeter will be in inches.
2. If the dimensions of a figure are in
centimeters, the perimeter will be in
centimeters. 3. If the dimensions of a
figure are in feet, the perimeter will be in
feet. Finding the perimeter of any polygon is
based on addition of measures. The perimeter of
some polygons can be expressed by a formula. 1.
PERIMETER OF A RECTANGLE Perimeter 2 x
Length 2 x Width or P 2 x L
2 x W or P 2 x (L W) 2. PERIMETER
OF A SQUARE Perimeter 4 x length of one
side or P S S S S or
P 4S 3. PERIMETER OF A TRIANGLE Perimeter
Side Side Side or P S S S
71
Plane/Plane Figure/Point
PLANETravel the same direction apart of every
point, so as never to meet, as lines, planes,
etc.Illustration PLANE FIGUREAll the
points of a figure lying on the same
plane.Illustration a b
c d
e POINTAn idea about an exact
location it has no dimensions whatsoever but is
represented by a dot () There is an unlimited
number of lines through a point.
Z
X
Q
Y
R
72
Polygon(Regular Polygon/Figure/Plane
Figures/Simple Closed Figure)
POLYGONA simple closed figure that consists only
of line segments. REGULAR POLYGON A polygon
with congruent sides and congruent angles.
FIGURE In Geometry, any sets of points.
PLANE FIGURES Rectangle, square and circle
are the most common. SIMPLE CLOSED FIGURE A
Simple Closed Figure is one that does not
intersect (cross) itself. If it is made up of
line segments it is called a polygon.
Illustration
73
Polygon (Parallelogram/Pentagon/Octagon/Quadrilate
ral/Rectangle)
PARALLELOGRAM A quadrilateral in which
opposite sides are parallel. PENTAGON A
polygon with five sides. OCTAGON An
eight-sided polygon. QUADRILATERAL A polygon
(simple closed figure) formed by four line
segments. RECTANGLE A quadrilateral (polygon)
with two pairs of parallel sides and four right
angles (4 sides and 4 square corners).
Illustration
74
Polygon (Square/Trapezoid)
SQUARE A quadrilateral (polygon) with
congruent sides the same length and four right
angles. Also, the product when a number is
multiplied by itself. Example 3 x 3 9,
The square of 3 or 3? Illustration
TRAPEZOID A quadrilateral (polygon) with
only one pair of parallel sides. Illustration
Z
Y
W
X
75
Polygon (Triangle)
TRIANGLE A figure (polygon) with three
sides. KINDS 1. EQUILATERAL TRIANGLE A
triangle all of whose sides are
congruent. 2. ISOSCELES TRIANGLE A triangle
with at least two sides congruent. 3.
RIGHT TRIANGLE A triangle with one right
angle. 4. SCALENE TRIANGLE A triangle with no
congruent sides. LEGS (of a right triangle)
The two sides in a right triangle that are
also sides of the right angles. Illustration
HYPOTENUSE The side opposite the
right angle in a right triangle.
76
Protractor/Prism/Ray
PROTRACTORAn instrument for measuring angles
just as a ruler is an instrument for measuring
line segments. PRISMA closed space figure. The
bases are congruent polygons in parallel
planes. RAY A point on a line and all the
points in one direction from the point.
Has infinite length and only one endpoint
(vertex). The sides of the
angle. Illustration
77
Region/Size/Space Figure/Straight Edge/Vertex
REGIONA closed curve and all the points inside
it. SIZERefers to the amount of opening between
the side (rays) of the angle. SPACE FIGUREA
figure encloses a part of space. STRAIGHT
EDGEHas no marks on it with which measurements
can be made by tracing along its edge one can
construct a line segment. VERTEXA common
endpoint of two rays, two segments, or three or
more edges of a space figure.Illustration
78
UNITS OF MEASURE
79
Length/Liquid/Weight
LENGTH ENGLISH METRIC 12 inches (in.)
1 foot (ft.) 1000 milliliters (mm) 1 meter
3 feet (ft.) 1 yard (yd.) 100
centiliters (cm) 1 meter 36 inches
1 yard (yd.) 10 deciliters (dm)
1 meter 5280 feet 1 mile
(MI.) 1000 liters 1
kilometer LIQUID ENGLISH METRIC 2 cups
(c.) 1 pint (pt.) 1000 milliliters
(ml) 1 liter (l) 2 pints 1
quart (qt.) 100 centiliters (cl) 1
liter (l) 4 quarts 1 gallon
(gal.) 10 deciliters (dl) 1 liter
(l) 1000 liters (l) 1
kiloliter (kl) WEIGHT ENGLISH METRIC 16
ounces (oz.) 1 pound (lb.) 1000 milligrams
(mg) 1 gram (g)2000 pounds 1
ton (T.) 100 centigrams (cg) 1 gram
10 decigrams (dg) 1 gram 1000 grams
1 kilogram
80
Equivalent Units/Time
EQUIVALENT UNITS LENGTH LIQUID
WEIGHT 2.5 centimeters is about 1 inch. .95
liter is about 1 quart. 28.35 grams
is about 1 ounce. .9 meter is about 1 yard.
3.79 liters is about 1 gallon.
.45 kilogram is about 1 pound. 1.6 kilometers
is about 1 mile. TIME 60 seconds
(sec.) 1 minute 60 minutes (min.)
1 hour 24 hours (hr.) 1 day 7
days 1 week (wk.) 365 days 1 year
(yr.) 366 days 1 leap year 10
years 1 decade 20 years 1
score 100 years 1 century