The science of geometry tells us what a triangle, square, cube is. In the modern world, it is studied in schools without exception. Also a science that studies directly what a triangle is and what its properties are, is trigonometry. She explores in detail all the phenomena associated with these geometric shapes. We will talk about what a triangle is today in our article. Below, their types will be described, as well as some theorems related to them.
What is a triangle? Definition
This is a flat polygon. It has three angles, which is clear from its name. It also has three sides and three peaks, the first of them are segments, the second are points. Knowing what the two angles are equal, you can find the third, taking the sum of the first two from the number 180.
What are triangles?
They can be classified according to various criteria.
First of all, they are divided into acute-angled, obtuse-angled and rectangular. The former have sharp angles, that is, those that are equal to less than 90 degrees. For obtuse angles, one of the angles is obtuse, that is, one that is more than 90 degrees, the other two are sharp. Equilateral triangles are also equilateral. For such triangles, all sides and angles are equal. All of them are equal to 60 degrees, this can be easily calculated by dividing the sum of all angles (180) by three.
Right triangle
It is impossible not to talk about what a right triangle is.
For such a figure, one angle is 90 degrees (straight), that is, two of its sides are perpendicular. The other two corners are sharp. They can be equal, then he will be isosceles. The Pythagorean theorem is connected with a right triangle. With its help, you can find a third party, knowing the first two. According to this theorem, if you add the square of one leg to the square of another, you can get the square of the hypotenuse. The square of the leg can be calculated by subtracting the square of the known leg from the hypotenuse square. Speaking of what a triangle is, one can recall the isosceles. This is one in which two of the sides are equal, and two angles are also equal.
What is cathetis and hypotenuse?
A leg is one of the sides of a triangle that form an angle of 90 degrees. Hypotenuse is the remaining side, which is located opposite a right angle. Perpendicular can be lowered from it onto the leg. The ratio of the adjacent leg to the hypotenuse is called nothing more than the cosine, and the opposite - the sine.
Egyptian triangle - what are its features?
It is rectangular. Its legs are three and four, and the hypotenuse is five. If you saw that the legs of this triangle are three and four, you can rest assured that the hypotenuse will be five. Also by this principle it can be easily determined that the leg will be three if the second is four and the hypotenuse five. To prove this statement, we can apply the Pythagorean theorem. If the two legs are 3 and 4, then 9 + 16 = 25, the root of 25 is 5, that is, the hypotenuse is 5. Also, the Egyptian triangle is called a right-angled triangle whose sides are 6, 8 and 10; 9, 12 and 15 and other numbers with a ratio of 3: 4: 5.
What else could a triangle be?
Triangles can also be inscribed and described. The figure around which the circle is described is called inscribed; all its vertices are points lying on the circle. The described triangle is the one into which the circle is inscribed. All its sides come into contact with it at certain points.
How is the area of the triangle?
The area of any figure is measured in square units (square meters, square millimeters, square centimeters, square decimeters, etc.) This value can be calculated in a variety of ways, depending on the type of triangle. The area of any shape with corners can be found if you multiply its side by a perpendicular dropped to it from the opposite corner, and dividing this figure by two. You can also find this value if you multiply two sides. Then multiply this number by the sine of the angle located between these sides, and divide it by two. Knowing all sides of the triangle, but not knowing its angles, you can find the area in another way. To do this, find half the perimeter. Then, in turn, subtract the different sides from the given number and multiply the four values obtained. Next, find the square root of the number that came out. The area of the inscribed triangle can be found by multiplying all sides and dividing the resulting number by the radius of the circle, which is described around it, multiplied by four.
The area of the described triangle is thus: half the perimeter is multiplied by the radius of the circle that is inscribed in it. If the triangle is equilateral, then its area can be found as follows: we square the side, multiply the resulting figure by the root of three, then divide this number by four. In a similar way, you can calculate the height of a triangle in which all sides are equal, for this one of them needs to be multiplied by the root of three, and then divide this number into two.
Triangle related theorems
The main theorems that are associated with this figure are the Pythagorean theorem described above, the theorems of sines and cosines. The second (sines) is that if you divide either side by the sine of the angle opposite to it, you can get the radius of the circle that is described around it, multiplied by two. The third (cosines) is that if you subtract their product multiplied by two and the cosine of the angle located between them from the sum of the squares of two sides, you get a square of the third side.
Dali Triangle - what is it?
Many, faced with this concept, at first think that this is some kind of definition in geometry, but this is not at all the case. The Dali Triangle is the common name for three places that are closely related to the life of a famous artist. The “peaks” of it are the house in which Salvador Dali lived, the castle that he gave to his wife, as well as a museum of surrealist paintings. During a tour of these places you can find out many interesting facts about this unique creative artist, known throughout the world.