Triangle is one of the basic shapes in geometry. It is customary to distinguish right triangles (one angle of which is equal to 900), acute and obtuse angles (angles less or more than 900 respectively), equilateral and isosceles.
When calculating various kinds, basic geometric concepts and quantities are used (sine, median, radius, perpendicular, etc.)
The topic for our study will be the height of an isosceles triangle. We will not delve into the terminology and definitions, we will only briefly outline the basic concepts that will be necessary to understand the essence.
So, an isosceles triangle is considered to be a triangle in which the size of the two sides is expressed by the same number (equality of sides). An isosceles triangle can be acute, obtuse, or right. It can also be equilateral (all sides of the figure are equal in size). You can often hear: all equilateral triangles are isosceles, but not allisosceles - equilateral.
The height of any triangle is the perpendicular dropped from the corner to the opposite side of the figure. The median is a segment drawn from the corner of the figure to the center of the opposite side.
What is remarkable about the height of an isosceles triangle?
- If the height dropped to one of the sides is a median and a bisector, then this triangle will be considered isosceles, and vice versa: a 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 height.
- The heights dropped on the lateral (equal) sides of an 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 on which this height was lowered, you can find out the area of this polygon. S=1/2 (chc)
How is the height of an isosceles triangle used in calculations? The properties of it drawn to its base make the following statements true:
- The main height, being at the same time the median, divides the base into two equal segments. This allows us to find out the value of the base, the area of the triangle formed by the height, etc.
- Being a perpendicular, the height of an isosceles triangle can be considered a side (leg) of a new right triangle. Knowing the size of each side, based on the Pythagorean theorem (allknown ratio of the squares of the legs and the hypotenuse), you 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 its 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 size of the angles and sides, the size of the sides, the area and the 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 give the formulas themselves, it is easy to find them. In addition, having a minimum of information, you can find the desired values and only after that proceed with the calculation of the height.
