altitude of a triangle Chapter 6 (p. 311)
The perpendicular segment from a vertex of a triangle to the opposite side or to the line that contains the opposite side
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 other words, it is a line that passes through one of the vertices of the triangle and is perpendicular to the opposite side.
The altitude of a triangle can be used to find the area of the triangle. The area of a triangle is equal to half the product of the base and the height (altitude) of the triangle.
To find the altitude of a triangle, we can use the following formula:
altitude = 2 * area / base
where area is the area of the triangle and base is the length of the base of the triangle.
Alternatively, we can use the Pythagorean theorem to find the length of the altitude. Let’s say the base of the triangle is b and the altitude is h. If we label the hypotenuse of the right triangle formed by the altitude, base, and a line segment connecting the vertex to the midpoint of the base as c, then we have:
c^2 = h^2 + (b/2)^2
Solving for h, we get:
h = sqrt(c^2 – (b/2)^2)
Once we have found the altitude of a triangle, we can use it to find the area of the triangle using the formula mentioned above.
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