What is the difference between the median and an altitude?

Question

Answer

Altitude:

An altitude of a triangle is the perpendicular drawn from a vertex to the opposite side of the vertex of the triangle. In the following triangle PQR, PS is perpendicular from the vertex P to QR. So, PS is an altitude of triangle PQR.

Median:

The line segment joining any vertex of a triangle to the mid-point of its opposite side is called the median of the triangle. In the following triangle ABC, D is the mid-point of side BC. So, AD is the median of the triangle.

Answer

Altitude means height of Resources taken Perpendicularly to the Base ... Median is a line taken from a fixed vertex to the midpoint of any resource. ..

Answer

If we take the given figure as TriangleMedian means the line joining the vertex and the midpoint of the opposite side Altitude means the height of the triangle and it is perpendicular, when the question is asked find altitude of the triangle then it means you should find the height of the triangle

Answer

Difference between the Median and an Altitude

Introduction:
In geometry, the median and altitude are both important concepts related to triangles. While they may seem similar, they serve different purposes and have distinct characteristics. Understanding the differences between the median and an altitude is crucial for a comprehensive understanding of triangles.

Median:
- Definition: A median of a triangle is a line segment that connects a vertex to the midpoint of the opposite side.
- Characteristics:
- A triangle has three medians, each connecting one vertex to the midpoint of the opposite side.
- The medians of a triangle intersect at a point called the centroid, which is located two-thirds of the distance from each vertex to the midpoint of the opposite side.
- The medians divide the triangle into six smaller triangles with equal areas.
- The lengths of the medians can be calculated using the formula: Median = (1/2) * sqrt(2 * (b^2 + c^2) - a^2), where a, b, and c are the lengths of the sides of the triangle.

Altitude:
- Definition: An altitude of a triangle is a line segment that extends from a vertex and is perpendicular to the opposite side or its extension.
- Characteristics:
- A triangle has three altitudes, each extending from one vertex to the opposite side or its extension and forming a right angle.
- The intersection point of the altitudes is called the orthocenter.
- The altitudes can be inside, outside, or on the triangle, depending on the type of triangle (acute, obtuse, or right).
- The length of an altitude can be calculated using the formula: Altitude = (2 * Area) / Base, where Area is the area of the triangle and Base is the length of the side to which the altitude is drawn.

Differences:
1. Definition: The median connects a vertex to the midpoint of the opposite side, while the altitude extends from a vertex and is perpendicular to the opposite side or its extension.
2. Intersection Point: The medians intersect at the centroid, whereas the altitudes intersect at the orthocenter.
3. Number: A triangle has three medians, but only three altitudes.
4. Divisions: The medians divide the triangle into six smaller triangles with equal areas, while the altitudes do not divide the triangle in this manner.
5. Calculations: The lengths of the medians can be calculated using a specific formula, while the length of an altitude depends on the area and the length of the base of the triangle.

Conclusion:
In conclusion, the median and altitude are both important concepts in geometry, specifically in relation to triangles. While the median connects a vertex to the midpoint of the opposite side and intersects at the centroid, the altitude extends from a vertex and is perpendicular to the opposite side or its extension, intersecting at the orthocenter. Understanding their definitions, characteristics, and differences enhances our comprehension of triangles and their properties.

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