What is the Difference Between Altitude and Perpendicular Bisector?
🆚 Go to Comparative Table 🆚The difference between altitude and perpendicular bisector can be understood through their definitions and properties:
- Altitude: An altitude of a triangle is a segment from a vertex to the line containing its opposite side, and is perpendicular to that line. It is a perpendicular segment in which one endpoint is at a vertex and the other endpoint is on the side opposite that vertex.
- Perpendicular Bisector: A perpendicular bisector is a line that passes through the midpoint of a segment and is perpendicular to that segment. It splits a segment into two congruent segments and is perpendicular to that segment.
In summary, an altitude is a perpendicular segment from a vertex to the opposite side of a triangle, while a perpendicular bisector is a line that passes through the midpoint of a segment and is perpendicular to it, splitting the segment into two congruent parts.
Comparative Table: Altitude vs Perpendicular Bisector
The main difference between an altitude and a perpendicular bisector is that an altitude is a line segment that connects a vertex of a triangle to the opposite side, while a perpendicular bisector is a line that passes through the midpoint of a side and is perpendicular to that side. Here is a comparison table of their differences:
| Feature | Altitude | Perpendicular Bisector |
|---|---|---|
| Definition | An altitude is a line segment connecting a vertex to the midpoint of the opposite side in a triangle. | A perpendicular bisector is a line passing through the midpoint of a side and is perpendicular to that side. |
| Position | One endpoint of an altitude is at a vertex, and the other endpoint is on the opposite side of the triangle. | A perpendicular bisector of a side goes through the vertex opposite that side. |
| Angle | The angle at the vertex where the altitude meets the triangle is always 90 degrees. | The angle between the perpendicular bisector and the side it is perpendicular to is always 90 degrees. |
| Midpoint | An altitude is a line segment joining a vertex of a triangle with the midpoint of the opposite side. | A perpendicular bisector is a line passing through the midpoint of a segment and is perpendicular to the segment. |
| Relationship | An altitude can also be a perpendicular bisector if it goes through the vertex opposite the side it is perpendicular to. | A perpendicular bisector can also be an altitude if it connects a vertex to the midpoint of the opposite side. |
In summary, an altitude connects a vertex to the midpoint of the opposite side, while a perpendicular bisector passes through the midpoint of a side and is perpendicular to that side. An altitude can also be a perpendicular bisector, and vice versa, depending on the specific triangle and its properties.
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