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1A plane figure with three straight sides and three angles.

*‘an equilateral triangle’**‘Cross-sections are in the shape of circles, ovals, squares, rectangles, equilateral triangles or regular polygons.’**‘He tested this intuition using two-dimensional plane figures - the triangle, square, pentagon, etc. - but this didn't work.’**‘The design radiates symmetrically from a central point and is constructed from a pattern of circles, equilateral triangles, squares, hexagons and/or six-pointed stars.’**‘Figure 6 shows an equilateral triangle and a rhombus that circumscribe the same unit circle.’**‘Using these simple tools they could construct equilateral triangles and hexagons and they could bisect any angle.’**‘He arranges thin rectangles, squares, triangles and trapezoids in complex patterns on the wall.’**‘This is constructed by dividing a line into three equal parts and replacing the middle segment by the other two sides of an equilateral triangle constructed on the middle segment.’**‘In this book Vernier gives a table of sines and a method for deriving the angles of a triangle if its sides are known.’**‘The back of a second, kneeling Magus and of the seated Virgin supporting the Child form two sides of an equilateral triangle located plumb in the centre of the design.’**‘A stationary front is denoted by semicircles and triangles on alternate sides of the front.’**‘The third regular polygon is the equilateral triangle, and two of them joined make a diamond.’**‘‘Art Deco was the first to come out with baguette diamonds, anything that had a straight line, triangles, trapezoids,’ he continued.’**‘For example, a level 1 question asked why a certain figure was an equilateral triangle.’**‘In the other case, the sides of the hexagon are parallel to the sides of the given triangle.’**‘Narayana gave the rules for the formation of doubly even, even and odd perfect magic squares along with magic triangles, rectangles and circles.’**‘A theorem of Riemann's geometry is that the sum of the interior angles of a triangle is always greater than 180 degrees, and increases as the areas of triangles increase.’**‘For example, we know that a circle is somehow more symmetrical than a equilateral triangle.’**‘Draw objects made entirely of triangles, rectangles or squares; make ‘butterfly’ pictures by painting on one half of the paper and folding it over so that the image is mirrored.’**‘In fact, it does not contain any straight line pieces at all: the middle third of any piece of straight line has been replaced by two sides of a triangle, creating a spike.’**‘For example, when we start with a hexagon, the final shape may be a segment, a triangle, or another hexagon.’*

**triangle**, tapered piece, segment, slice, section- 1.1A thing shaped like a triangle.
*‘a small triangle of grass’**‘Here, the ligament is assumed to be formed on an enlarging triangle that maintains its shape during growth.’**‘The ear ornaments in this collection are geometrically complex in design, combining squares, circles and triangles into single forms.’**‘It was a white triangle with a red border and a black exclamation mark inside and had to be pasted on the windshield and the back window of the cars driven by inexperienced drivers.’**‘Free-range pigs have shelters shaped as triangles or half circles, but most porkers were lurking inside; pine trees had snow plastered on the north side of their trunks and the hot sun on the south side.’**‘First flowing south, then north, the river has shaped a dramatic triangle with an area of about 50 square kilometres.’**‘All that remains of the madhouse is a triangle of grass.’**‘It is rare to see objects against a background of a square, a triangle, and oval shapes.’**‘There is a huge expanse of sweeping railway track that links up to form a triangle enclosing acres of scrub and grass.’**‘The domes consisted of a series of linked triangles forming a sphere that proved to be so strong that it could be built with very lightweight materials and remain structurally sound in virtually any size.’**‘The weather map symbol for a cold front is a blue line with triangles pointing the direction the cold air is moving.’**‘A cold front is shown by a line with blue triangles pointing in the direction the front is travelling.’**‘If an animal's center of mass falls outside the triangle of support formed by its three feet on the ground, it is statically unstable and will fall.’**‘For example, the letter A in a triangle should be plainly marked on a fire extinguisher that can be used for ordinary combustibles.’**‘She connected the lines, forming a triangle through the crumbs.’**‘Ashton was sitting in the corner of the bench between the arm and the back with his legs bent forming a triangle with the seat.’**‘She pointed at two sets of three claw marks arranged in a triangle, with a streak in the blood on the floor between them.’**‘In Exhibit 2 below, we have July coffee trading at 58 cents, which is indicated by the black triangle along the horizontal axis.’**‘Wood blinds, meanwhile, can fit a variety of applications, including quarter arches, full arches, angles, trapezoids, hexagons and triangles.’**‘We have to do two sides of a triangle, straight at the waves and then back at an angle to avoid capsizing but we make it to the Peat Lough, moor up in the reeds and fish out into deep water.’**‘Cut the remaining slices into triangles or rectangles to cover the sides of the bowl.’*

- 1.2A situation involving three people or things, especially an emotional relationship involving a couple and a third person with whom one of them is involved.
*‘In a triangle, the three relationships are interdependent; they are not three separate person-to-person dyads.’**‘The third person in the triangle is receiving affection and intimacy that rightfully belongs to the spouse.’**‘And nothing is quite so potent an activator of consciousness as a relationship triangle.’**‘When my character fell for one of the farmers and got involved in a love triangle, it was all very scandalous.’**‘It was more of a straightforward kung fu movie, featuring a love triangle, a couple of betrayals, and a revenge plot.’**‘In fact, everyone involved in the romantic triangle is noble.’**‘A theatre critic's secretary is caught up in a love triangle involving the stars of a production of Othello after she is persuaded to alter a review to make it more favourable.’**‘Another war movie cliché is the love triangle, involving a conveniently-placed nurse.’**‘Poor Gabby was stuck in the middle of a love triangle with two emotionally unstable men.’**‘This, however, can lead to their wives feeling unsupported, creating a schism in the marital relationship - something the three players in the triangle would want to avoid.’**‘My pose was slightly more complicated because of my character's complex relationship triangle.’**‘It's a lush, romantic epic about lovers in a fatal emotional triangle, set against the backdrop of the Spanish Civil War.’**‘Through rhythmic, rhymed language, both groups express the frustrations and joys of love: falling in love, heartbreak, jealousy, love triangles.’*

- 1.3A musical instrument consisting of a steel rod bent into a triangle and sounded by being struck with a small steel rod.
*‘We were given drums, triangles, maracas and tambourines to experiment with.’**‘As she lay trembling slightly for a long moment, not daring to breathe, she became aware of a faint humming, like the sound that a triangle makes after you strike it.’**‘It was the first time I ever heard a recorded triangle that didn't sound false.’**‘He started to tap it, making a small ting, much like the sound of a musical triangle.’**‘We hear the cellist playing cymbal and mark tree and the violinist playing triangle and drum.’**‘A gong, cymbals, a triangle, and a timpani, as well as the pentatonic scale, create a sense of the Far East.’**‘A triangle chimes in the background; it's all very bittersweet.’**‘The school's year four and five class got to work with drums, xylophones and triangles.’**‘The children moved on to the Salvation Army Sunday School, where she learnt to play the triangle and cymbals.’**‘There are grunts, an accompanying triangle, and even something like be-bop drums.’**‘Towards the end of the show, Lieberman hands out percussion instruments - triangles, chimes, shakers - and has no trouble finding volunteers to take the instruments.’**‘The triangle for once doesn't play as if afraid it will never be heard from again, while the piccolo stands out for its cleanliness of tone and brilliance.’**‘She lifted the chunky Celtic cross which perpetually weighed her neck down and flicked it with a finger as if it was a musical triangle to show it was made of pure, die cast metal.’**‘Traditionally, Seychellois performed their music on drums, violins, accordions, and the triangle.’**‘Chapter Two demonstrates ways props, such as drums, sticks, triangles, balls, a trampoline, hoops, bells and scarves, can be used to intensify rhythmic feeling.’**‘We decided to make a percussion supergroup with me on the triangle, but after a couple of minutes and ringing ears we realised that this wasn't the best thing to do for our sanity.’*

**trio**, triplet, triplets, triumvirate, triad, trinity, troika, triunity, triangle, triplex - 1.4A frame used to position the balls in pool and snooker.
*‘He racked up a triangle of pool balls at the proper end of the table, and he began to practice his pool shots.’**‘This trophy, made of Waterford Crystal and in the shape of a snooker frame triangle, is a new one because the previous cup was sponsored by a tobacco company and their link with sport ended two seasons ago.’**‘Only the shape of the rack of balls is a triangle.’**‘Sean pitched his drink down on the bar table and picked up the triangle to racket the balls.’**‘‘Try it,’ he said after he gathered all of the balls into the triangle.’**‘I broke the triangle, getting two balls into a pocket.’**‘Walking over toward the table and bending down I adjusted myself to correctly break the triangle of balls before me that Zea had just finished racking.’**‘Stephan picked the triangle up from its position on the floor and placed it carefully on the table.’**‘Kath broke the triangle of balls pretty successfully although none of them went in.’**‘Viviane arranged the balls in the triangle as she continued to speak.’**‘I watched as he broke the triangle of balls at the far end of the table into a huge mess.’*

- 1.5North American A drawing instrument in the form of a right triangle.
*‘Use a triangle to lay out the outline of the label, a vertical center line, and horizontal guidelines for the height of the lettering.’**‘Use a triangle to line those up and see that they're at right angles, then draw across them using the grid ruler.’*

- 1.6
**triangles**historical A frame of three halberds joined at the top to which a soldier was bound for flogging.*‘Sage had screamed at every blow, but now hung unconscious from the triangle, while Cruttwell was taking his flogging in silence.’**‘For a flogging, three halberds would be bound in an upright triangle, with a fourth tied horizontally across at chest height.’*

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