Which segment is an altitude of the triangle

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. The altitude of a triangle is the perpendicular distance from the base to the opposite vertex. It can be located either outside or inside the triangle depending on the type of triangle. The median of a triangle is the line segment drawn from the vertex to the opposite side that divides a triangle into two equal parts. It bisects the base of the triangle and always lies inside the triangle.

Yes, the altitude of a triangle is a perpendicular line segment drawn from a vertex of a triangle to the base or the side opposite to the vertex. Yes, the altitude of a triangle is also referred to as the height of the triangle. It is denoted by the small letter 'h' and is used to calculate the area of a triangle. Here, the 'height' is the altitude of the triangle. No, the altitude of an obtuse triangle lies outside the triangle because the angle opposite to the vertex from which the altitude is drawn is an obtuse angle.

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. In Figure , the altitude drawn from the vertex angle of an isosceles triangle can be proven to be a median as well as an angle bisector. A line segment is drawn from the vertex to the opposite side of a triangle such that it is perpendicular to the side and bisects the side in two equal parts then it is said to be the altitude of an equilateral triangle.

The altitude of a right triangle divides the right-angled triangle into two similar triangles. According to the right triangle altitude theorem, the altitude drawn from the vertex on the hypotenuse is equal to the geometric mean of line segments formed by altitude on hypotenuse.

In the isosceles triangle which have two of its sides congruent its altitude bisects the angle of the vertex and bisects the base. Triangle Type.