How many altitudes does a right triangle have

Figure 2 In a right triangle, each leg can serve as an altitude. Figure 4 The three lines containing the altitudes intersect in a single point,. A median in a triangle is the line segment drawn from a vertex to the midpoint of its opposite side. Every triangle has three medians. In Figure 5 , E is the midpoint of BC. In every triangle, the three medians meet in one point inside the triangle Figure 6.

An angle bisector in a triangle is a segment drawn from a vertex that bisects cuts in half that vertex angle. Every triangle has three angle bisectors. In every triangle, the three angle bisectors meet in one point inside the triangle Figure 8.

In general, altitudes, medians, and angle bisectors are different segments. In certain triangles, though, they can be the same segments. Since there are three sides in a triangle, three altitudes can be drawn in it. Different triangles have different kinds of altitudes. The altitude of a triangle which is also called its height is used in calculating the area of a triangle and is denoted by the letter 'h'.

The altitude of a triangle is the perpendicular line segment drawn from the vertex of the triangle to the side opposite to it. The altitude makes a right angle with the base of the triangle that it touches. It is commonly referred to as the height of a triangle and is denoted by the letter 'h'. It can be measured by calculating the distance between the vertex and its opposite side.

It is to be noted that three altitudes can be drawn in every triangle from each of the vertices. Observe the following triangle and see the point where all the three altitudes of the triangle meet. This point is known as the 'Orthocenter'. The altitudes of various types of triangles have some properties that are specific to certain triangles. 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. Right Triangle Altitude Theorem Part a: The measure of the altitude drawn f rom the vertex of the right angle of a right triangle to its hypotenuse is the geometric mean between the measures of the two segments of the hypotenuse.

Find the area of the triangle use the geometric mean. In your notebook, list the three similar triangles, and next to each triangle, list its hypotenuse. Print the sketch and add it to your notebook.