decision of geometrical problems requires a tremendous amount of knowledge.One of the fundamental definitions of this science is a right-angled triangle.
Under this concept implies a geometrical figure consisting of three angles and sides, and the value of one of the angles of 90 degrees.The parties that make up the right angle are called legs of the third hand, which is opposed to it, is called the hypotenuse.
If the legs are in this figure are equal, it is called an isosceles right triangle.In this case there is a species belonging to two triangles, and hence the properties observed in both groups.Recall that the angles at the base of an isosceles triangle are always absolutely hence the sharp corners of the figure would include 45 degrees.
one of the following characteristics suggests that a right triangle is equal to another:
- legs of two triangles are equal;
- figures have the same hypotenuse and one of the legs;
- equal to the hypotenuse, and any sharp corners;
- observed the condition of equality of the leg and an acute angle.
area of a right triangle is calculated as easily using standard formulas, and as a value equal to half the product of the other two sides.
In a right triangle observed following relations:
- leg is nothing else than the average proportional to the hypotenuse and its projection on it;
- if describe a right triangle around the circle, its center will be in the middle of the hypotenuse;
- height drawn from the right angle, is proportional to the average projections of the legs of the triangle at its hypotenuse.
interesting is that whatever the right-angled triangle, these properties are always respected.
Pythagorean theorem
addition to the above properties of right triangles is typical for the following conditions: the square of the hypotenuse equals the sum of the squares of the other two sides.This theorem is named after its founder - the Pythagorean theorem.He opened this ratio when engaged in studying the properties of squares constructed on the sides of a right triangle.
To prove the theorem we construct a triangle ABC, whose legs are denoted by a and b, and the hypotenuse c.Next, we construct two squares.One side will be the hypotenuse, the other the sum of the two legs.
Then the area of the first square will be found in two ways: as the sum of the areas of four triangles ABC and second square, or the square of the parties, of course, that these ratios are equal.That is:
C2 + 4 (ab / 2) = (a + b) 2, convert the resulting expression:
C2 + 2 ab = a2 + b2 + 2 ab
As a result, we get c2 = a2 + b2
Thus, the right-angled triangle geometric figure corresponds not only to all the properties characteristic triangles.The presence of a right angle leads to the fact that the figure has other unique relations.Their study is useful not only in science but also in everyday life, as such a figure as a right triangle is found everywhere.
