altitude of a triangle Chapter 6 (p. 311)
The altitude of a triangle is a line segment that is perpendicular to the base of the triangle and connects the base to the opposite vertex
The altitude of a triangle is a line segment that is perpendicular to the base of the triangle and connects the base to the opposite vertex. In simple words, it is a line that extends from one of the vertices of a triangle to the opposite side, forming a right angle with the base.
To understand this concept better, let’s consider an example. Take a triangle ABC, where side AC is the base. The altitude of the triangle can be drawn from vertex B to side AC. This line segment will be perpendicular to side AC and will create a right angle at point B.
The altitude divides the triangle into two smaller triangles. In our example, the triangle ABC is divided into triangle ABD and triangle CBD. The length of the altitude is called the height of the triangle.
The altitude of a triangle has several important properties:
1. The length of the altitude is always shorter than the length of the side it is drawn to.
2. The altitude can lie inside, outside, or on the triangle, depending on the type of triangle.
3. The altitude, the base, and the vertex to which the altitude is drawn form a right triangle.
4. The altitudes of a triangle are concurrent, meaning they intersect at one point called the orthocenter.
Altitudes are useful in solving various problems related to triangles, such as finding the area of a triangle or determining properties of similar triangles.
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