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What is the difference between median of a triangle and the altitude of a triangle?
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Understanding the Median of a Triangle
The median of a triangle is a line segment that connects a vertex to the midpoint of the opposite side. Each triangle has three medians, and they all intersect at a point called the centroid. The centroid divides each median into two segments, with the segment connecting the centroid to the vertex being twice as long as the segment connecting the centroid to the midpoint.
Understanding the Altitude of a Triangle
The altitude of a triangle is a perpendicular line segment drawn from a vertex to the line that contains the opposite side. Each triangle has three altitudes, and they may or may not lie within the triangle, depending on the triangle's type (acute, right, or obtuse).
Key Differences
The median of a triangle is a line segment that connects a vertex to the midpoint of the opposite side. Each triangle has three medians, and they all intersect at a point called the centroid. The centroid divides each median into two segments, with the segment connecting the centroid to the vertex being twice as long as the segment connecting the centroid to the midpoint.
- The median divides the triangle into two smaller triangles of equal area.
- It is always located inside the triangle, regardless of the type of triangle.
- The formula for finding the length of the median can vary depending on the triangle's coordinates.
Understanding the Altitude of a Triangle
The altitude of a triangle is a perpendicular line segment drawn from a vertex to the line that contains the opposite side. Each triangle has three altitudes, and they may or may not lie within the triangle, depending on the triangle's type (acute, right, or obtuse).
- The altitude represents the height of the triangle from a specific vertex.
- It is crucial for calculating the area of the triangle, as Area = 1/2 × base × height.
- The intersection of the altitudes is called the orthocenter, which can lie inside or outside the triangle.
Key Differences
- Definition: Median connects a vertex to the midpoint of the opposite side; altitude connects a vertex to the opposite side perpendicularly.
- Location: Medians are always within the triangle; altitudes can be inside or outside.
- Purpose: Medians help find the centroid; altitudes help calculate area.
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What is the difference between median of a triangle and the altitude of a triangle?
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What is the difference between median of a triangle and the altitude of a triangle? for Class 7 2024 is part of Class 7 preparation. The Question and answers have been prepared according to the Class 7 exam syllabus. Information about What is the difference between median of a triangle and the altitude of a triangle? covers all topics & solutions for Class 7 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the difference between median of a triangle and the altitude of a triangle?.
What is the difference between median of a triangle and the altitude of a triangle? for Class 7 2024 is part of Class 7 preparation. The Question and answers have been prepared according to the Class 7 exam syllabus. Information about What is the difference between median of a triangle and the altitude of a triangle? covers all topics & solutions for Class 7 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the difference between median of a triangle and the altitude of a triangle?.
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