A triangle is one of the main figures in geometry. It is customary to single out triangles straight (one angle at which is 90 0 ), acute and obtuse (the angles are less than or greater than 90 0, respectively), equilateral and isosceles.
In calculations of various kinds, basic geometric concepts and quantities are used (sine, median, radius, perpendicular, etc.)
The theme for our study will be the height of an isosceles triangle. We will not delve into the terminology and definitions, we only briefly outline the basic concepts that will be necessary for understanding the essence.
So, it is customary to consider an isosceles triangle to be a triangle in which the magnitude of two sides is expressed by the same number (equality of sides). An isosceles triangle can be acute-angled, and obtuse, and straight. It can also be equilateral (all sides of the figure are equal in magnitude). You can often hear: all equilateral triangles isosceles, but not all isosceles triangles are equilateral.
The height of any triangle is considered to be a perpendicular, lowered from the corner to the opposite side of the figure. The segment drawn from the corner of the figure to the center of the opposite side is the median.
What is remarkable for the height of the isosceles triangle?
- If the height dropped to one of the sides is the median and bisector, then this triangle will be considered isosceles, and vice versa: the triangle is isosceles, if the height dropped to one of the sides is both a bisector and a median. This height is called the main.
- The heights lowered to the lateral (equal) sides of the isosceles triangle are identical and form two similar figures.
- If you know the height of an isosceles triangle (as, indeed, of any other) and the side to which this height was lowered, you can find out the area of this polygon. S = 1/2 * (c * h c )
How is the height of an isosceles triangle used in calculations? The properties of it, conducted to its foundation, make the following statements true:
- The main height, being both a median, divides the base into two equal segments. This allows us to find out the size of the base, the area of the triangle formed by height, etc.
- Being a perpendicular, the height of an isosceles triangle can be considered the side (leg) of a new rectangular triangle. Knowing the size of each side, based on the Pythagorean theorem (the well-known ratio of the squares of the legs and the hypotenuse), we can calculate the numerical value of the height.
What is the height of the triangle? In general, an isosceles triangle, the height of which we need, does not cease to be such in essence. Therefore, for him, all the formulas used for these figures, as such, do not lose their relevance. You can calculate the length of the height, knowing the magnitude of the angles and sides, the magnitude of the sides, the area and side, as well as a number of other parameters. The height of the triangle is equal to a certain ratio of these values. It does not make sense to bring the formulas themselves; it is simple to find them. In addition, having a minimum of information, you can find the desired values and after that proceed to calculate the height.