Triangle Sum Theorem Proof
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triangle
As noun
a closed plane figure having three sides and three angles
a flat triangular piece, usually of plastic, with straight edges, used in connection with a T square for drawing perpendicular lines, geometric figures, etc
any three-cornered or three-sided figure, object, or piece:a triangle of land
a musical percussion instrument that consists of a steel triangle, open at one corner, that is struck with a steel rod
a group of three; triad
a situation involving three persons, especially one in which two of them are in love with the third
(initial capital letter) Astronomy
the constellation Triangulum
sum
As noun
the aggregate of two or more numbers, magnitudes, quantities, or particulars as determined by or as if by the mathematical process of addition:The sum of and is
a particular aggregate or total, especially with reference to money:The expenses came to an enormous sum
an indefinite amount or quantity, especially of money:to lend small sums
a series of numbers or quantities to be added up
an arithmetical problem to be solved, or such a problem worked out and having the various steps shown
the full amount, or the whole
the substance or gist of a matter, comprehensively or broadly viewed or expressed:the sum of his opinions
concise or brief form:in sum
Mathematics
the limit of the sequence of partial sums of a given infinite series
union (def a)
a summary
As verb (used with object), summed, summing
to combine into an aggregate or total (often followed by up)
to ascertain the sum of, as by addition
to bring into or contain in a small compass (often followed by up)
As verb (used without object), summed, summing
to amount (usually followed by to or into):Their expenses summed into the thousands
As Verb phrases
sum up, to reckon: We summed up our assets and liabilities
to bring into or contain in a brief and comprehensive statement; summarize: to sum up the case for the prosecution
to form a quick estimate of: I summed him up in a minute
theorem
As noun
Mathematics
a theoretical proposition, statement, or formula embodying something to be proved from other propositions or formulas
a rule or law, especially one expressed by an equation or formula
Logic
a proposition that can be deduced from the premises or assumptions of a system
an idea, belief, method, or statement generally accepted as true or worthwhile without proof
proof
As noun
evidence sufficient to establish a thing as true, or to produce belief in its truth
anything serving as such evidence:What proof do you have?
the act of testing or making trial of anything; test; trial:to put a thing to the proof
the establishment of the truth of anything; demonstration
Law
(in judicial proceedings) evidence having probative weight
the effect of evidence in convincing the mind
an arithmetical operation serving to check the correctness of a calculation
Mathematics, Logic
a sequence of steps, statements, or demonstrations that leads to a valid conclusion
a test to determine the quality, durability, etc
, of materials used in manufacture
Distilling
the arbitrary standard strength, as of an alcoholic liquor
strength with reference to this standard: “ proof” signifies a proof spirit, usually % alcohol
Photography
a trial print from a negative
Printing
a trial impression, as of composed type, taken to correct errors and make alterations
one of a number of early and superior impressions taken before the printing of the ordinary issue: to pull a proof
(in printmaking) an impression taken from a plate or the like to show the quality or condition of work during the process of execution; a print pulled for examination while working on a plate, block, stone, etc
Numismatics
one of a limited number of coins of a new issue struck from polished dies on a blank having a polished or matte surface
the state of having been tested and approved
proved strength, as of armor
Scots Law
the trial of a case by a judge alone, without a jury
As adjective
able to withstand; successful in not being overcome:proof against temptation
impenetrable, impervious, or invulnerable:proof against outside temperature changes
used for testing or proving; serving as proof
of standard strength, as an alcoholic liquor
of tested or proven strength or quality:proof armor
noting pieces of pure gold and silver that the U
S
assay and mint offices use as standards
As verb (used with object)
to test; examine for flaws, errors, etc
; check against a standard or standards
Printing
prove (def )
to proofread
to treat or coat for the purpose of rendering resistant to deterioration, damage, etc
(often used in combination):to proof a house against termites; to shrink-proof a shirt
Cookery
to test the effectiveness of (yeast), as by combining with warm water so that a bubbling action occurs
to cause (especially bread dough) to rise due to the addition of baker's yeast or other leavening
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