Median and Altitude of Triangle
Median and Altitude of Triangle
Median and altitude of triangle: A median is a line segment drawn from the vertex of a triangle to the midpoint of the opposite side of triangle. As in a triangle there are three vertices and three sides, therefore there are three medians in each triangle. From each vertex we can draw a line joining the midpoint of the opposite side of the triangle. It divides the opposite side into two equal line segments. In the figure AE is a median as E is the midpoint of the side BC. Thus BE = EC
Altitude: An altitude is a perpendicular line segment drawn from a vertex of a triangle to the opposite side. There are three altitudes in a triangle as there are three vertices and three side. In the figure AD is the altitude from vertex A. AD is perpendicular to BC.
Theorem: Show that median of a triangle divides it into two triangles of equal area. Given: A triangle ABC with AE as the median To Prove: ar ( Construction: Draw AD Proof:
As AE is a median From Eq (1) and (2) ar ( Hence Proved. |  |
ILLUSTRATION: In the figure E is the mid point of the median AD of triangle ABC. Prove that:
Solution: It is given that AD is the median we know that the median divides the triangle into two triangles of equal area
Also E is the midpoint of AD. Therefore AE is the median of triangle ABD Using equation 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. | |||
| Right Option : A | |||
| View Explanation | |||
The area of a triangle is 50 square units. The length of the altitude is _______ if the length of the base is 10 units. | |||
| Right Option : C | |||
| View Explanation | |||
If ABC is a triangle and AD is its median lying on the side BC, then | |||
| Right Option : B | |||
| View Explanation | |||
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