used before a singular noun to mean one of a group, when it is not a particular one
From this reading Fix your card on a piece of paper and draw the equilateral triangle BCF, BF and CF being equal to BC.
(quantifier) used with either mass or count nouns to indicate the whole number or amount of or every one of a class
From this reading The reason for this is more obvious in the solution I have given than in any other method that I have seen, and (although the problem may be solved with all the working on the cardboard) that is partly why I have preferred it.
in addition
From this reading Also mark off the point G so that DG shall equal DC.
in spite of the fact that
From this reading The reason for this is more obvious in the solution I have given than in any other method that I have seen, and (although the problem may be solved with all the working on the cardboard) that is partly why I have preferred it.
used to join words or parts of a sentence that go together
From this reading Fix your card on a piece of paper and draw the equilateral triangle BCF, BF and CF being equal to BC.
one or some or every or all without specification
From this reading The reason for this is more obvious in the solution I have given than in any other method that I have seen, and (although the problem may be solved with all the working on the cardboard) that is partly why I have preferred it.
at the same time that; because; in the way that
From this reading Draw the line CG and produce it until it cuts the line BF in H. If we now make HA parallel to BE, then A is the point from which our cut must be made to the corner D, as indicated by the dotted line.
BCadverbUS /ˌbiːˈsiː/
before the Christian era; used following dates before the supposed year Christ was born
From this reading Fix your card on a piece of paper and draw the equilateral triangle BCF, BF and CF being equal to BC.
BCF
Dictionary entry pending editorial verification. Tap Listen to hear the word.
From this reading Fix your card on a piece of paper and draw the equilateral triangle BCF, BF and CF being equal to BC.
used with a past participle to form the passive, or with -ing for continuous tenses
From this reading Draw the line CG and produce it until it cuts the line BF in H. If we now make HA parallel to BE, then A is the point from which our cut must be made to the corner D, as indicated by the dotted line.
beingauxiliary verbUS /ˈbiːɪŋ/
the -ing form of “be”
From this reading Fix your card on a piece of paper and draw the equilateral triangle BCF, BF and CF being equal to BC.
BF
Dictionary entry pending editorial verification. Tap Listen to hear the word.
From this reading Fix your card on a piece of paper and draw the equilateral triangle BCF, BF and CF being equal to BC.
showing who or what does the action
From this reading Draw the line CG and produce it until it cuts the line BF in H. If we now make HA parallel to BE, then A is the point from which our cut must be made to the corner D, as indicated by the dotted line.
one of a set of small pieces of stiff paper marked in various ways and used for playing games or for telling fortunes
From this reading Fix your card on a piece of paper and draw the equilateral triangle BCF, BF and CF being equal to BC.
cardboardnounUS /ˈkɑːrdbɔːrd/
a stiff moderately thick paper
From this reading The reason for this is more obvious in the solution I have given than in any other method that I have seen, and (although the problem may be solved with all the working on the cardboard) that is partly why I have preferred it.
CDnounUS /ˌsiːˈdiː/
a soft bluish-white ductile malleable toxic bivalent metallic element; occurs in association with zinc ores
From this reading A curious point in connection with this problem is the fact that the position of the point A is independent of the side CD.
CFnoun
a radioactive transuranic element; discovered by bombarding curium with alpha particles
From this reading Fix your card on a piece of paper and draw the equilateral triangle BCF, BF and CF being equal to BC.
CG
Dictionary entry pending editorial verification. Tap Listen to hear the word.
From this reading Draw the line CG and produce it until it cuts the line BF in H. If we now make HA parallel to BE, then A is the point from which our cut must be made to the corner D, as indicated by the dotted line.
a relation between things or events (as in the case of one causing the other or sharing features with it)
From this reading A curious point in connection with this problem is the fact that the position of the point A is independent of the side CD.
a place off to the side of an area
From this reading Draw the line CG and produce it until it cuts the line BF in H. If we now make HA parallel to BE, then A is the point from which our cut must be made to the corner D, as indicated by the dotted line.
beyond or deviating from the usual or expected
From this reading A curious point in connection with this problem is the fact that the position of the point A is independent of the side CD.
separate with or as if with an instrument
From this reading Draw the line CG and produce it until it cuts the line BF in H. If we now make HA parallel to BE, then A is the point from which our cut must be made to the corner D, as indicated by the dotted line.
cutsnounUS /kʌts/
plural of “cut” — a share of the profits
From this reading Draw the line CG and produce it until it cuts the line BF in H. If we now make HA parallel to BE, then A is the point from which our cut must be made to the corner D, as indicated by the dotted line.
a fat-soluble vitamin that prevents rickets
From this reading Draw the line CG and produce it until it cuts the line BF in H. If we now make HA parallel to BE, then A is the point from which our cut must be made to the corner D, as indicated by the dotted line.
DCnounUS /ˌdiːˈsiː/
the district occupied entirely by the city of Washington; chosen by George Washington as the site of the capital of the United States and created out of land ceded by Maryland and Virginia
From this reading Also mark off the point G so that DG shall equal DC.
DGnoun
1/10 gram
From this reading Also mark off the point G so that DG shall equal DC.
dottedadjectiveUS /ˈdɑːtəd/
having a pattern of dots
From this reading Draw the line CG and produce it until it cuts the line BF in H. If we now make HA parallel to BE, then A is the point from which our cut must be made to the corner D, as indicated by the dotted line.
cause to move by pulling
From this reading Fix your card on a piece of paper and draw the equilateral triangle BCF, BF and CF being equal to BC.
be identical or equivalent to
From this reading Fix your card on a piece of paper and draw the equilateral triangle BCF, BF and CF being equal to BC.
equilateralnoun
a figure whose sides are all equal
From this reading Fix your card on a piece of paper and draw the equilateral triangle BCF, BF and CF being equal to BC.
a piece of information about circumstances that exist or events that have occurred
From this reading A curious point in connection with this problem is the fact that the position of the point A is independent of the side CD.
FixverbUS /fɪks/
restore by replacing a part or putting together what is torn or broken
From this reading Fix your card on a piece of paper and draw the equilateral triangle BCF, BF and CF being equal to BC.
intended to be given to, or used by, somebody
From this reading The reason for this is more obvious in the solution I have given than in any other method that I have seen, and (although the problem may be solved with all the working on the cardboard) that is partly why I have preferred it.
showing where something starts, or who sent it
From this reading Draw the line CG and produce it until it cuts the line BF in H. If we now make HA parallel to BE, then A is the point from which our cut must be made to the corner D, as indicated by the dotted line.
a metric unit of weight equal to one thousandth of a kilogram
From this reading Also mark off the point G so that DG shall equal DC.
givenadjectiveUS /ˈɡɪvən/
acknowledged as a supposition
From this reading The reason for this is more obvious in the solution I have given than in any other method that I have seen, and (although the problem may be solved with all the working on the cardboard) that is partly why I have preferred it.
a nonmetallic univalent element that is normally a colorless and odorless highly flammable diatomic gas; the simplest and lightest and most abundant element in the universe
From this reading Draw the line CG and produce it until it cuts the line BF in H. If we now make HA parallel to BE, then A is the point from which our cut must be made to the corner D, as indicated by the dotted line.
(astronomy) the angular distance of a celestial point measured westward along the celestial equator from the zenith crossing; the right ascension for an observer at a particular location and time of day
From this reading Draw the line CG and produce it until it cuts the line BF in H. If we now make HA parallel to BE, then A is the point from which our cut must be made to the corner D, as indicated by the dotted line.
haveauxiliary verbUS /hæv/
used with a past participle to form the perfect tenses
From this reading The reason for this is more obvious in the solution I have given than in any other method that I have seen, and (although the problem may be solved with all the working on the cardboard) that is partly why I have preferred it.
the person speaking or writing, as the subject of the verb
From this reading The reason for this is more obvious in the solution I have given than in any other method that I have seen, and (although the problem may be solved with all the working on the cardboard) that is partly why I have preferred it.
on condition that; in the event that
From this reading Draw the line CG and produce it until it cuts the line BF in H. If we now make HA parallel to BE, then A is the point from which our cut must be made to the corner D, as indicated by the dotted line.
inside something, or within a place, period, or state
From this reading Draw the line CG and produce it until it cuts the line BF in H. If we now make HA parallel to BE, then A is the point from which our cut must be made to the corner D, as indicated by the dotted line.
independentadjectiveUS /ˌɪndɪˈpendənt/
free from external control and constraint
From this reading A curious point in connection with this problem is the fact that the position of the point A is independent of the side CD.
indicatedverbUS /ˈɪndəkeɪtəd/
past form of “indicate” — be a signal for or a symptom of
From this reading Draw the line CG and produce it until it cuts the line BF in H. If we now make HA parallel to BE, then A is the point from which our cut must be made to the corner D, as indicated by the dotted line.
the form of “be” used with he, she, it, or a singular noun
From this reading Draw the line CG and produce it until it cuts the line BF in H. If we now make HA parallel to BE, then A is the point from which our cut must be made to the corner D, as indicated by the dotted line.
a thing, animal, or idea already mentioned
From this reading Draw the line CG and produce it until it cuts the line BF in H. If we now make HA parallel to BE, then A is the point from which our cut must be made to the corner D, as indicated by the dotted line.
a formation of people or things one beside another
From this reading Draw the line CG and produce it until it cuts the line BF in H. If we now make HA parallel to BE, then A is the point from which our cut must be made to the corner D, as indicated by the dotted line.
produced by a manufacturing process
From this reading Draw the line CG and produce it until it cuts the line BF in H. If we now make HA parallel to BE, then A is the point from which our cut must be made to the corner D, as indicated by the dotted line.
engage in
From this reading Draw the line CG and produce it until it cuts the line BF in H. If we now make HA parallel to BE, then A is the point from which our cut must be made to the corner D, as indicated by the dotted line.
attach a tag or label to
From this reading Also mark off the point G so that DG shall equal DC.
used to say something is possible, or to give permission
From this reading The reason for this is more obvious in the solution I have given than in any other method that I have seen, and (although the problem may be solved with all the working on the cardboard) that is partly why I have preferred it.
a way of doing something, especially a systematic way; implies an orderly logical arrangement (usually in steps)
From this reading The reason for this is more obvious in the solution I have given than in any other method that I have seen, and (although the problem may be solved with all the working on the cardboard) that is partly why I have preferred it.
(comparative of “much” used with mass nouns) a quantifier meaning greater in size or amount or extent or degree
From this reading The reason for this is more obvious in the solution I have given than in any other method that I have seen, and (although the problem may be solved with all the working on the cardboard) that is partly why I have preferred it.
used to say something is necessary, or almost certainly true
From this reading Draw the line CG and produce it until it cuts the line BF in H. If we now make HA parallel to BE, then A is the point from which our cut must be made to the corner D, as indicated by the dotted line.
in the historical present; at this point in the narration of a series of past events
From this reading Draw the line CG and produce it until it cuts the line BF in H. If we now make HA parallel to BE, then A is the point from which our cut must be made to the corner D, as indicated by the dotted line.
obviousadjectiveUS /ˈɑːbviəs/
easily perceived by the senses or grasped by the mind
From this reading The reason for this is more obvious in the solution I have given than in any other method that I have seen, and (although the problem may be solved with all the working on the cardboard) that is partly why I have preferred it.
belonging to, or connected with, somebody or something
From this reading Fix your card on a piece of paper and draw the equilateral triangle BCF, BF and CF being equal to BC.
from a particular thing or place or position (“forth” is obsolete)
From this reading Also mark off the point G so that DG shall equal DC.
touching and supported by a surface
From this reading Fix your card on a piece of paper and draw the equilateral triangle BCF, BF and CF being equal to BC.
not the same one or ones already mentioned or implied
From this reading The reason for this is more obvious in the solution I have given than in any other method that I have seen, and (although the problem may be solved with all the working on the cardboard) that is partly why I have preferred it.
belonging to the speaker and others
From this reading Draw the line CG and produce it until it cuts the line BF in H. If we now make HA parallel to BE, then A is the point from which our cut must be made to the corner D, as indicated by the dotted line.
a material made of cellulose pulp derived mainly from wood or rags or certain grasses
From this reading Fix your card on a piece of paper and draw the equilateral triangle BCF, BF and CF being equal to BC.
parallelnounUS /ˈperəlel/
something having the property of being analogous to something else
From this reading Draw the line CG and produce it until it cuts the line BF in H. If we now make HA parallel to BE, then A is the point from which our cut must be made to the corner D, as indicated by the dotted line.
to some extent; in some degree; not wholly
From this reading The reason for this is more obvious in the solution I have given than in any other method that I have seen, and (although the problem may be solved with all the working on the cardboard) that is partly why I have preferred it.
a separate part of a whole
From this reading Fix your card on a piece of paper and draw the equilateral triangle BCF, BF and CF being equal to BC.
a geometric element that has position but no extension
From this reading Also mark off the point G so that DG shall equal DC.
the particular portion of space occupied by something
From this reading A curious point in connection with this problem is the fact that the position of the point A is independent of the side CD.
more desirable than another
From this reading The reason for this is more obvious in the solution I have given than in any other method that I have seen, and (although the problem may be solved with all the working on the cardboard) that is partly why I have preferred it.
problemnounUS /ˈprɑːbləm/
a state of difficulty that needs to be resolved
From this reading A curious point in connection with this problem is the fact that the position of the point A is independent of the side CD.
bring forth or yield
From this reading Draw the line CG and produce it until it cuts the line BF in H. If we now make HA parallel to BE, then A is the point from which our cut must be made to the corner D, as indicated by the dotted line.
a rational motive for a belief or action
From this reading The reason for this is more obvious in the solution I have given than in any other method that I have seen, and (although the problem may be solved with all the working on the cardboard) that is partly why I have preferred it.
inflected form of “see” — perceive by sight or have the power to perceive by sight
From this reading The reason for this is more obvious in the solution I have given than in any other method that I have seen, and (although the problem may be solved with all the working on the cardboard) that is partly why I have preferred it.
used with I and we for the future, or to offer and suggest
From this reading Also mark off the point G so that DG shall equal DC.
a place within a region identified relative to a center or reference location
From this reading A curious point in connection with this problem is the fact that the position of the point A is independent of the side CD.
for that reason; with the result that
From this reading Also mark off the point G so that DG shall equal DC.
solutionnounUS /səˈluːʃən/
a homogeneous mixture of two or more substances; frequently (but not necessarily) a liquid solution
From this reading The reason for this is more obvious in the solution I have given than in any other method that I have seen, and (although the problem may be solved with all the working on the cardboard) that is partly why I have preferred it.
solvedadjectiveUS /sɑːlvd/
explained or answered
From this reading The reason for this is more obvious in the solution I have given than in any other method that I have seen, and (although the problem may be solved with all the working on the cardboard) that is partly why I have preferred it.
used to introduce the second part of a comparison
From this reading The reason for this is more obvious in the solution I have given than in any other method that I have seen, and (although the problem may be solved with all the working on the cardboard) that is partly why I have preferred it.
used to introduce what somebody said, thought, or felt
From this reading Also mark off the point G so that DG shall equal DC.
used before a noun that is already known, already mentioned, or the only one of its kind
From this reading Fix your card on a piece of paper and draw the equilateral triangle BCF, BF and CF being equal to BC.
subsequently or soon afterward (often used as sentence connectors)
From this reading Draw the line CG and produce it until it cuts the line BF in H. If we now make HA parallel to BE, then A is the point from which our cut must be made to the corner D, as indicated by the dotted line.
used for a person or thing that is near, or that has just been mentioned
From this reading A curious point in connection with this problem is the fact that the position of the point A is independent of the side CD.
used before the base form of a verb to make the infinitive
From this reading Fix your card on a piece of paper and draw the equilateral triangle BCF, BF and CF being equal to BC.
trianglenounUS /ˈtraɪæŋɡəl/
a three-sided polygon
From this reading Fix your card on a piece of paper and draw the equilateral triangle BCF, BF and CF being equal to BC.
untilprepositionUS /ənˈtɪl/
up to a particular time
From this reading Draw the line CG and produce it until it cuts the line BF in H. If we now make HA parallel to BE, then A is the point from which our cut must be made to the corner D, as indicated by the dotted line.
the speaker together with one or more other people
From this reading Draw the line CG and produce it until it cuts the line BF in H. If we now make HA parallel to BE, then A is the point from which our cut must be made to the corner D, as indicated by the dotted line.
used to introduce a clause giving more about a thing just mentioned
From this reading Draw the line CG and produce it until it cuts the line BF in H. If we now make HA parallel to BE, then A is the point from which our cut must be made to the corner D, as indicated by the dotted line.
the cause or intention underlying an action or situation, especially in the phrase “the whys and wherefores”
From this reading The reason for this is more obvious in the solution I have given than in any other method that I have seen, and (although the problem may be solved with all the working on the cardboard) that is partly why I have preferred it.
in the company of; together with
From this reading A curious point in connection with this problem is the fact that the position of the point A is independent of the side CD.
actively engaged in paid work
From this reading The reason for this is more obvious in the solution I have given than in any other method that I have seen, and (although the problem may be solved with all the working on the cardboard) that is partly why I have preferred it.
belonging to the person or people being spoken to
From this reading Fix your card on a piece of paper and draw the equilateral triangle BCF, BF and CF being equal to BC.