# 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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