Difference between altitude and median of a triangle

Question

Hey there! 👋 Geometry can be tricky, right? Especially when you're juggling altitudes and medians in triangles. 🤔 They sound similar, but they're totally different! Let's break it down so it sticks!

anne.andrews · Accepted Answer

📚 Understanding Altitude and Median of a Triangle

Let's explore the altitude and median of a triangle. While both are line segments drawn from a vertex, they serve different purposes and have distinct properties. Think of it this way: the altitude is all about height, while the median is all about bisecting the base.

📐 Definition of Altitude
The altitude of a triangle is a line segment drawn from a vertex perpendicular to the opposite side (or its extension). It represents the height of the triangle from that vertex.

📏 Definition of Median
The median of a triangle is a line segment drawn from a vertex to the midpoint of the opposite side. It divides that side into two equal segments.

📊 Altitude vs. Median: A Detailed Comparison

Feature
      Altitude
      Median

Definition
      A line segment from a vertex perpendicular to the opposite side.
      A line segment from a vertex to the midpoint of the opposite side.

Angle with the Opposite Side
      Forms a 90-degree angle (perpendicular).
      Does not necessarily form a 90-degree angle.

Bisection of Opposite Side
      Does not necessarily bisect the opposite side.
      Always bisects the opposite side.

Location
      Can be inside, outside, or on the triangle (in the case of a right triangle).
      Always inside the triangle.

Number in a Triangle
      Each triangle has three altitudes, one from each vertex.
      Each triangle has three medians, one from each vertex.

Point of Concurrency
      Altitudes intersect at the orthocenter.
      Medians intersect at the centroid.

Special Properties
      Related to the area and height of the triangle.
      Divides the triangle into two triangles of equal area.

✨ Key Takeaways

📏 Definition:
    The altitude is about height (perpendicular), while the median is about bisecting the opposite side.
  📐 Angle:
 The altitude forms a right angle, while the median generally does not.
  ➗ Bisection:
The median bisects the opposite side, while the altitude does not necessarily.
📍 Location:
The altitude can be outside the triangle, while the median is always inside.

Difference between altitude and median of a triangle

1 Answers

📚 Understanding Altitude and Median of a Triangle

📐 Definition of Altitude

📏 Definition of Median

📊 Altitude vs. Median: A Detailed Comparison

✨ Key Takeaways

Join the discussion

Feature	Altitude	Median
Definition	A line segment from a vertex perpendicular to the opposite side.	A line segment from a vertex to the midpoint of the opposite side.
Angle with the Opposite Side	Forms a 90-degree angle (perpendicular).	Does not necessarily form a 90-degree angle.
Bisection of Opposite Side	Does not necessarily bisect the opposite side.	Always bisects the opposite side.
Location	Can be inside, outside, or on the triangle (in the case of a right triangle).	Always inside the triangle.
Number in a Triangle	Each triangle has three altitudes, one from each vertex.	Each triangle has three medians, one from each vertex.
Point of Concurrency	Altitudes intersect at the orthocenter.	Medians intersect at the centroid.
Special Properties	Related to the area and height of the triangle.	Divides the triangle into two triangles of equal area.