Trapeze is a quadrilateral with two parallel sides, which are the bases, and two non-parallel sides, which are the sides.
There are also names such as isosceles or isosceles.
It is a trapezoid with right angles on the lateral side.
Trapeze elements
a, b bases of a trapezoid(a parallel to b ),
m, n sides trapeze,
d 1 , d 2 — diagonals trapeze,
h- height trapezoid (a segment connecting the bases and at the same time perpendicular to them),
MN- middle line (a segment connecting the midpoints of the sides).
Trapezium area
- Through half the sum of the bases a, b and the height h : S = \frac(a + b)(2)\cdot h
- Through the midline MN and height h : S = MN\cdot h
- Through the diagonals d 1 , d 2 and the angle (\sin \varphi ) between them: S = \frac(d_(1) d_(2) \sin \varphi)(2)
Trapezoid Properties
Median line of the trapezoid
middle line parallel to the bases, equal to their half-sum, and divides each segment with ends located on straight lines that contain the bases (for example, the height of the figure) in half:
MN || a, MN || b, MN = \frac(a + b)(2)
The sum of the angles of a trapezoid
The sum of the angles of a trapezoid, adjacent to each side, is equal to 180^(\circ) :
\alpha + \beta = 180^(\circ)
\gamma + \delta =180^(\circ)
Equal area triangles of a trapezoid
Equal-sized, that is, having equal areas, are the segments of the diagonals and the triangles AOB and DOC formed by the sides.
Similarity of formed trapezoid triangles
similar triangles are AOD and COB, which are formed by their bases and diagonal segments.
\triangle AOD \sim \triangle COB
similarity coefficient k is found by the formula:
k = \frac(AD)(BC)
Moreover, the ratio of the areas of these triangles is equal to k^(2) .
The ratio of the lengths of segments and bases
Each segment connecting the bases and passing through the point of intersection of the diagonals of the trapezoid is divided by this point in relation to:
\frac(OX)(OY) = \frac(BC)(AD)
This will also be true for the height with the diagonals themselves.
Aerial gymnastics, one of the types of circus gymnastics, is designed to demonstrate the skills of artists working on special equipment and devices. Many elements of gymnastics have been known since antiquity in various countries East, the main basis modern technology aerial gymnasts was formed and consolidated by circus performers in the early twentieth century.
The arsenal of aerial gymnastics includes work with trapeziums, rings, canvases and other structures suspended at a certain height. Structures can be both static and moving.
Tricks in aerial gymnastics are performed either solo by one artist, or by a group of artists on various devices suspended above the circus arena. It is worth mentioning the main instruments of aerial gymnasts - bamboo, frame, trapezoid, rings, loops, etc.
The genre of aerial gymnastics also includes numbers with stunt flights of artists from trapeze to trapeze or from trapeze to the hands of a catcher. Aerial flights among aerialists are considered a difficult and risky part of aerial gymnastics, accessible only to true masters of their craft.
Voltigeurs must be able to evenly distribute muscular energy, have an ideal eye, finely feel the metro-rhythm, have professional courage, courage and impeccable plastique.
The genre of aerial gymnastics is based on the demonstration of outstanding body control skills, significantly exceeding the capabilities of an ordinary person.
The work of aerialists is akin to the work of stuntmen, because aerialists risk not only their health, but also their lives, showing the most daring tricks. Without risky tricks, the limit of human capabilities, the strength of the spirit and the plasticity of the body cannot be shown.
In the circus show, the aerial gymnastics genre is recognized as the most intense and spectacular. Spectators tickle their nerves and see everything with their own eyes here and now. Often high-class aerialists work without insurance, they are supported only by the disturbing roll of the snare drum in the orchestra. Fragile girls often show not only beauty and plasticity, but also perform complex power elements in the air that require significant muscular effort.
Spectacular performances of aerial gymnasts are preceded by a titanic work with material that the average person does not see and about which the audience only very vaguely guess. The daily training of gymnasts is associated with trauma, bruises and calluses, and only fanatics remain in the world of aerial gymnastics. gravity daily work, training, classes, tailoring of costumes, creation of special air props and rental of the venue, the artists decide at their own expense, which is very difficult to do in times of economic crises. Nevertheless, obstacles do not stop real artists and the best gymnasts break through to their fans in any way, presenting a class of work, despite hundreds of large and thousands of small, domestic, everyday problems and inconveniences.
Today, the possibilities of aerial gymnastics are that rare trump card that organizers of entertainment and entertainment events can use and use. Amateur dance at the pole and singing karaoke in last years surprise no one. A serious guest of a hotel, restaurant, exhibition will remember only the brightest performances of artists, everything else, "budget art" will only make a sophisticated audience, seriously versed in art, sports and show business, laugh.
The trapezoid is a metal crossbar 60-65 cm long (up to 90 cm in flight) and 25-30 mm in diameter. For a more comfortable grip, the crossbar is wrapped with braid, and the gymnasts rub their hands with magnesia. Ropes are attached to the edges of the crossbar (with a thin cable inside for strength), the ends of which are hooked on the stem. Outside, the ropes are decorated with braid or bandage. The length of the ropes can be adjusted, usually it does not exceed 4 m. Trapezes used in flights are suspended from the standard not on ropes, but on thin cables.
Trapezoids are single, double and group. The single trapezoid is used for the female solo performance. It demonstrates exercises performed in the hang and in support. The most characteristic hang on the knees, "flag" on one hand, balancing on the back, back planche, turns around the trapezoid, as well as various "cliffs" on the knees, on the heels, on the toes. "Cliffs" are also more complex, for example: "cliff" in socks from an emphasis on the neck, "cliff" on the knees from a position standing on a trapezoid in swing, "cliff" in socks from balancing on the back in swing.
Many tricks, such as hanging on heels, on toes, "cliffs", are more often performed on a swinging trapeze, as they are more spectacular. Demonstration of exercises of a dynamic nature is called a performance on the shvung trap.
The traditional final number on a single trapezoid is loping (from the English "looping the loop" - a dead loop) - rotation around the stem. There are several ways of such rotation, for example, standing tall, catching on special protrusions (pins) on the soles of the shoes for the slots of the rotating sleeve, put on the stem.
Another way is to rotate on a rigid trapezoid, that is, on a trapezoid that has solid metal lines on the sides instead of ropes or cables. (For the first time this trick was shown by the Bulgarian artist L. Dobrich in 1905). Having developed a circular rotation in one direction, he then transferred the rotation in the opposite direction.
Literature:
3.B. Gurevich, On the genres of the Soviet circus, M., 1977.
- Upper - adjoins the neck, is responsible for lifting the shoulders up.
- Middle - between the shoulder blades, is involved in the rise of the shoulder blades.
- Lower - in the lower part of the shoulder blades, is responsible for lowering the shoulder blades in the lower phase of movement.
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The main functions of the trapezium are the movement of the shoulders in the vertical and horizontal plane, tilting the head back, and also lifting the shoulder blades up.
Keeping the trapezoid in good shape is necessary for any athlete. This will increase your strength output in basic exercises, reduce the load on the shoulder joints and ligaments, reduce the curvature of the spine in the cervical region and minimize the risk of damage and injury to the entire shoulder girdle.
- Shrugs are rightfully considered the best exercise for developing the trapezoid, but many athletes do them wrong. You can not include biceps and forearms in the work. Wrist straps help to cope with this very well. The elbows should be almost completely extended throughout the approach, then the load will fall purposefully on the trapezoid.
- Do not use too much working weight. When training the trapezius muscles, it is much more important to work in full amplitude and feel the maximum muscle contraction at the top point, lingering there for 1-2 seconds.
- Do not press your chin to your chest when performing shrugs. This increases the compression of the cervical spine and can lead to injury.
- Trapeze loves pumping. To properly bleed these muscles, use supersets, combining shrugs of any variation with pulling movements that also involve the shoulders, such as close-grip chin rows. Another option to increase the intensity is to do dropsets at the end of each set: reduce the working weight and without rest do another set or two with a lighter weight.
- Trapeze is a relatively small muscle group, it is enough to train it once a week. It is optimal to combine it with a back or shoulder workout. To make the entire shoulder girdle look massive, do not forget to pay enough attention to your deltas and neck muscles as well. If you notice that the trapeze has begun to overtake the shoulders in development, which visually makes the figure less wide in the shoulder girdle, just stop doing separate exercises for this muscle group.
- Trapeze workouts should be short but intense. As a rule, one or two exercises are enough to work out this muscle group. Alternate different movements in each workout and perform them in a different order, then you will make progress faster.
- Watch your posture. Often, stoop in the cervical and thoracic spine does not allow you to fully train the trapezoid. The athlete simply cannot perform the desired movement in full amplitude and feel muscle contraction.
- Train moderately. Overtraining of the trapezius muscles will lead to a deterioration in blood circulation in the muscles of the neck and the entire cervical spine. This is fraught with an increase in intracranial pressure, headaches and dizziness.
- Shrugs do not involve rotation of the shoulder joints at the top. For some reason, many novice athletes sin with this. When using heavy weights, this rotation becomes one of the most damaging movements for your rotator cuff. The correct trajectory of movement implies raising and lowering the weight in the same plane, there should not be any extraneous movements.
The best exercises for working out trapeze
Now let's look at exercises that will help you achieve maximum results when working out the trapezius muscles.
Shrugs with a barbell
- This is the main exercise for the mass of trapezium. Their upper part works mainly here, since when lifting the bar is located in front of you. The movement should be amplitude, as if at the top point you are trying to reach your ears with your shoulders. In this movement, you can work with a fairly large weight, so you can better feel the stretch in the muscles at the bottom point. If necessary, use wrist straps and an athletic belt.
Use a medium grip at shoulder width to keep your shoulders out of the work. When lifting, keep the bar as close to the body as possible and minimize cheating - this method will do nothing but increase the risk of injury to the movement. An alternative option is shrugs in Smith.
- This is an exercise on the upper part of the trapezoid. Here it is recommended to use less weight, but do more repetitions, so you can more easily achieve intense pumping (blood filling of the muscles).
Since the hands are turned parallel to each other in this exercise, the forearms are actively involved in the work. So concentrate on keeping your arms straight and not bending your elbows. Then you will lift the dumbbells with the effort of the trapezium, and not with your hands. You can also use straps.
To turn dumbbell shrugs into a mid-lower trapezoid exercise, sit on a bench and lean forward slightly:
This will change the load vector, and you will bring your shoulder blades closer together at the top. Due to this, most of the load will go to the middle and lower parts of the trapezius muscles.
Shrugs in the simulator
For this exercise, you will need a lower block and a wide handle. Keeping your back straight, pull your shoulders up and slightly back. The biomechanics of the movement is different from the movements in classic barbell shrugs. By pulling your shoulders back, you load the middle part of the trapezium and the rear bundles of the deltoid muscles more. Because of this, the back of the upper back will look more massive and bumpy. In addition, the device of the block simulator predetermines a stronger stretching of the muscles at the bottom point, which only increases the efficiency of this exercise.
Shrugs with a barbell behind your back
This is a great exercise for the middle and lower trapezoid. It is not entirely suitable for beginners, as it requires a developed muscular frame and good stretching of the shoulder joints.
For convenience, this exercise is recommended to be performed in the Smith machine. At the bottom point, relax all the muscles of the shoulder girdle a little to lower the barbell as low as possible. But do not forget to keep the lumbar spine perfectly straight. The closer to your back you bring the bar as you lift, the harder the trapezoid will work. A further position will put more stress on the rear delts.
Barbell row to the chin with a narrow grip
- This is a basic exercise in which both the trapeze and shoulders work. In this exercise, it is important to take a fairly narrow grip and keep the elbow above the level of the hand, then you will be able to work in full amplitude and load the entire area of \u200b\u200bthe trapezius muscles. The wider you take, the more load goes to the middle deltas.
Alternate exercises: close grip Smith chin row, narrow grip two dumbbell chin row, kettlebell chin row.
Deadlift
A review of the exercises would be incomplete without a mention. Even its variety is not so important, whether it be classic, sumo, trap bar deadlift, Romanian deadlift or dumbbell deadlift. In this exercise, there is almost no dynamic load on the muscle group of interest to us, but the trapezium carries the most powerful static stress throughout the entire approach. Experienced athletes work with serious weights in this exercise, this determines the further growth of the trapezium. Therefore, it is powerlifters who, more often than others, can boast of impressive trapezes, without even doing separate exercises for this muscle group.
The trapezoid also bears part of the load when performing any horizontal rows for the thickness of the back: or, lower block and others, as well as when using a narrow grip in vertical rods (pull-ups, pull-ups, upper block pulls, etc.). Indirectly, the load falls on the trapezoid and during many exercises for the deltoid muscles, for example, swings with dumbbells while standing, sitting or tilted, with a wide grip, abducting the arms in the simulator to the back deltoid and others.
Trapezius muscle training program
There is no fundamental difference between trapezoid training during periods of muscle mass gain and drying. All exercises (except the deadlift) are relatively isolated, and can be used at any stage of the training.
Training a trapezoid in the gym is a rather simple task. Pick a couple of exercises that work best for you and consistently improve your performance using various load progression methods. Use the following chart as a guide:
To fruitfully train trapeze at home, a minimum set of equipment is enough: barbells or dumbbells. An approximate version of a home trapezoid workout is as follows:
Many athletes also train trapeziums on the horizontal bars and parallel bars, performing an imitation of a shrug in the hang. These movements are more static, the amplitude is strictly limited, and it will not be easy to feel the isolated work of the trapezium in them. However, you can try to replace them with strength training if you do not have the opportunity to do weights.
Lesson topic
Trapeze
Lesson Objectives
Continue introducing new definitions in geometry;
To consolidate knowledge about the already studied geometric shapes;
Introduce the formulation and proofs of the properties of a trapezoid;
To teach the use of the properties of various figures in solving problems and performing tasks;
Continue to develop attention in students, logical thinking and mathematical speech;
Cultivate interest in the subject.
Lesson objectives
To arouse interest in knowledge of geometry;
Continue to exercise students in solving problems;
Arouse cognitive interest in the lessons of mathematics.
Lesson plan
1. Repeat the material studied earlier.
2. Acquaintance with the trapezoid, its properties and features.
3. Solving problems and completing tasks.
Repetition of previously studied material
In the previous lesson, you got acquainted with such a figure as a quadrilateral. Let's consolidate the material covered and answer the questions posed:
1. How many angles and sides does a 4-gon have?
2. Formulate the definition of a 4-gon?
3. What is the name of the opposite sides of the 4-gon?
4. What types of quadrangles do you know? List them and define each one.
5. Draw an example of a convex and non-convex quadrilateral.
Trapeze. General properties and definition
A trapezoid is a quadrangular figure in which only one pair of opposite sides is parallel.
AT geometric definition A trapezoid is a 4-gon that has two parallel sides and the other two do not.
The name of such an unusual figure as "trapezoid" comes from the word "trapezion", which is translated from Greek, denotes the word "table", from which the word "meal" and other related words also originate.
In some cases in a trapezoid, a pair of opposite sides is parallel, while its other pair is not parallel. In this case, the trapezoid is called curvilinear.
Trapeze elements
The trapezoid consists of such elements as the base, side lines, middle line and its height.
The base of a trapezoid is called its parallel sides;
The lateral sides are called the other two sides of the trapezoid, which are not parallel;
The midline of a trapezoid is called a segment that connects the midpoints of its sides;
The height of a trapezoid is the distance between its bases.
Types of trapezium
Exercise:
1. Formulate the definition of an isosceles trapezoid.
2. What trapezoid is called rectangular?
3. What does an acute-angled trapezoid mean?
4. Which trapezoid is obtuse?
General properties of a trapezoid
Firstly, the middle line of the trapezoid is parallel to the base of the figure and is equal to its half-sum;
Secondly, the segment that connects the midpoints of the diagonals of a 4-angled figure is equal to the half-difference of its bases;
Thirdly, in a trapezoid, parallel lines that intersect the sides of the angle of a given figure cut off proportional segments from the sides of the angle.
Fourth, in any type of trapezoid, the sum of the angles adjacent to its side is 180°.
Where else is there a trapezoid
The word "trapezoid" is present not only in geometry, it has a wider application in Everyday life.
This is unusual word we can meet while watching sports competitions of gymnasts performing acrobatic exercises on the trapeze. In gymnastics, a trapezoid is called a sports equipment, which consists of a crossbar suspended on two ropes.
Also, this word can be heard while working out in the gym or among people who are engaged in bodybuilding, since trapeze is not only geometric figure or a sports acrobatic apparatus, but also powerful back muscles, which are located behind the neck.
The figure shows an aerial trapeze, which was invented for circus acrobats by artist Julius Leotard back in the nineteenth century in France. At first, the creator of this number set his projectile at a low height, but in the end it was moved under the very dome of the circus.
Aerialists in the circus perform tricks of flights from trapeze to trapeze, perform cross flights, do somersaults in the air.
In equestrian sport, trapezoid is a stretching exercise or stretching of the horse's body, which is very beneficial and pleasant for the animal. During the horse's stance in the trapezoid position, stretching the legs of the animal or the muscles of its back works. We can observe this beautiful exercise during the bow or the so-called "front crunch", when the horse bends deeply.
Task: Give your examples of where else in everyday life you can hear the words "trapeze"?
Did you know that for the first time in 1947, the famous French fashion designer Christian Dior produced a fashion show in which there was a silhouette of an A-line skirt. And although more than sixty years have passed, this silhouette is still in fashion, and does not lose its relevance to this day.
In the wardrobe of the English queen, the A-line skirt has become an indispensable item and her hallmark.
Reminiscent of the geometric shape of a trapezoid, the skirt of the same name goes well with any blouses, blouses, tops and jackets. The classic and democratic style of this popular style allows you to wear it with strict jackets and slightly frivolous tops. In such a skirt it would be appropriate to appear both in the office and at a disco.
Problems with a trapezoid
To facilitate solving problems with trapezoids, it is important to remember a few basic rules:
First, draw two heights: BF and CK.
In one of the cases, as a result you will get a rectangle - ВСФК from which it is clear that FC=BC.
AD=AF+FK+KD, hence AD=AF+BC+KD.
In addition, it is immediately obvious that ABF and DCK are right triangles.
Another option is possible when the trapezoid is not quite standard, where
AD=AF+FD=AF+FK–DK=AF+BC–DK.
But the easiest option is if our trapezoid is isosceles. Then it becomes even easier to solve the problem, because ABF and DCK are right triangles, and they are equal. AB = CD, since the trapezoid is isosceles, and BF = CK, as the height of the trapezoid. From the equality of triangles follows the equality of the corresponding sides.