They are as follows:. Let us learn how to find out the altitude of a scalene triangle, equilateral triangle, right triangle, and isosceles triangle. The important formulas for the altitude of a triangle are summed up in the following table.
The following section explains these formulas in detail. A scalene triangle is one in which all three sides are of different lengths. To find the altitude of a scalene triangle, we use the Heron's formula as shown here.
A triangle in which two sides are equal is called an isosceles triangle. The altitude of an isosceles triangle is perpendicular to its base. Let us see the derivation of the formula for the altitude of an isosceles triangle.
One of the properties of the altitude of an isosceles triangle that it is the perpendicular bisector to the base of the triangle. A triangle in which all three sides are equal is called an equilateral triangle. Let us see the derivation of the formula for the altitude of an equilateral triangle. When we construct an altitude of a triangle from a vertex to the hypotenuse of a right-angled triangle, it forms two similar triangles.
It is popularly known as the Right triangle altitude theorem. Let us see the derivation of the formula for the altitude of a right triangle. The altitude of an obtuse triangle lies outside the triangle. It is usually drawn by extending the base of the obtuse triangle as shown in the figure given below.
We know that the median and the altitude of a triangle are line segments that join the vertex to the opposite side of a triangle.
However, they are different from each other in many ways. Observe the figure and the table given below to understand the difference between the median and altitude of a triangle. Example 1: The area of a triangle is 72 square units. Find the length of the altitude if the length of the base is 9 units. Example 2: Calculate the length of the altitude of a scalene triangle whose sides are 7 units, 8 units, and 9 units respectively.
Let us name the sides of the scalene triangle to be 'a', 'b', and 'c' respectively. Example 3: Calculate the altitude of an isosceles triangle whose two equal sides are 8 units and the third side is 6 units. In an isosceles triangle the altitude is:. The altitude of a triangle is a line segment that is drawn from the vertex of a triangle to the side opposite to it. It is perpendicular to the base or the opposite side which it touches. Since there are three sides in a triangle , three altitudes can be drawn in a triangle.
All the three altitudes of a triangle intersect at a point called the 'Orthocenter'. The altitude of a triangle can be calculated according to the different formulas defined for the various types of triangles.
The formulas used for the different triangles are given below:. The altitude of a triangle is the line drawn from a vertex to the opposite side of a triangle. The important properties of the altitude of a triangle are as follows:. When an altitude is drawn from a vertex to the hypotenuse of a right-angled triangle, it forms two similar triangles. A triangle in which all three sides are unequal is a scalene triangle. The altitude of a triangle and median are two different line segments drawn in a triangle.
For more on this, see Orthocenter of a triangle. The following two pages demonstrate how to construct the altitude of a triangle with compass and straightedge. Constructing the altitude of a triangle altitude inside. Constructing the altitude of a triangle altitude outside. In the animation at the top of the page: Drag the point A and note the location of the altitude line. Drag it far to the left and right and notice how the altitude can lie outside the triangle.
Drag B and C so that BC is roughly vertical. Drag A. Notice how the altitude can be in any orientation, not just vertical. Go to Constructing the altitude of a triangle and practice constructing the altitude of a triangle with compass and ruler. Home Contact About Subject Index. Try this Drag the orange dots on each vertex to reshape the triangle.
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