ORTHOCENTER
Definition of Orthocenter
The point of intersection of the altitudes of a triangle is called an orthocenter.
More about Orthocenter
Orthocenter of an obtuse triangle lies outside the triangle.
Orthocenter of an acute triangle lies inside the triangle.
Orthocenter of a right triangle lies on the triangle.
Example of Orthocenter
In the figure, AD, BE, and CF are the altitudes drawn from the vertices A, B, and C respectively. The point of intersection of these altitudes is 'H'. So, 'H' is the orthocenter of the triangle ABC.
Solved Example on Orthocenter
In a right-angled triangle, the orthocenter lies
Choices:
A. at the vertex containing the right angle
B. outside the triangle
C. at the midpoint of the hypotenuse
D. inside the triangle
Correct Answer: A
Solution:
Step 1:
Step 2: Orthocenter is the point of intersection of the altitudes. Each leg in a right triangle forms an altitude.
Step 3: So, in a right-angled triangle, the orthocenter lies at the vertex containing the right angle.
Related Terms for Orthocenter
Altitude
Point of Intersection
Triangle
Quick Summary
- The orthocenter is the point where all three altitudes of a triangle intersect.
- The location of the orthocenter depends on the type of triangle: acute (inside), obtuse (outside), right (on the vertex of the right angle).
🍎 Teacher Insights
Use dynamic geometry software to demonstrate how the orthocenter changes as the vertices of the triangle are moved. Emphasize the relationship between the type of triangle and the orthocenter's location.🎓 Prerequisites
- Triangles
- Altitude of a Triangle
- Point of Intersection
Check Your Knowledge
Q1: In a right-angled triangle, where does the orthocenter lie?
Frequently Asked Questions
Q: Where does the orthocenter lie in a right triangle?
A: The orthocenter of a right triangle lies at the vertex containing the right angle.
Q: Where does the orthocenter lie in an obtuse triangle?
A: The orthocenter of an obtuse triangle lies outside the triangle.