Altitude and Median in an Isosceles Triangle

An isosceles triangle is a triangle that has two sides of equal length. In an isosceles triangle, the altitude and the median from the same vertex are the same line segment.

Definition of Altitude and Median

- Altitude: The altitude of a triangle is a line segment drawn from a vertex perpendicular to the opposite side.
- Median: The median of a triangle is a line segment drawn from a vertex to the midpoint of the opposite side.

Explanation

In an isosceles triangle, two sides are equal in length. Let's assume these sides are AB and AC, and the remaining side is BC. The vertex where the two equal sides meet is called vertex A.

When we draw the altitude from vertex A to the side BC, it will be perpendicular to BC and will bisect BC at D (the midpoint of BC).

Similarly, when we draw the median from vertex A to the side BC, it will also pass through the midpoint D of BC.

Since the altitude and the median both pass through the midpoint of BC, they will be the same line segment.

Example

Let's consider an isosceles triangle ABC where AB = AC. We draw the altitude from vertex A to side BC and label the intersection point as D. We also draw the median from vertex A to side BC and label the intersection point as E.

- The altitude AD is perpendicular to BC and bisects BC at D.
- The median AE also passes through D, which is the midpoint of BC.

Therefore, in an isosceles triangle, the altitude and median from the same vertex are the same line segment. Thus, the correct answer is option 'B' - Isosceles Triangle.