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### Course: Geometry (all content)>Unit 4

Lesson 7: Altitudes

# Common orthocenter and centroid

If the orthocenter and centroid are the same point, then the triangle is equilateral. This is because the orthocenter is the intersection of the altitudes, which are also the medians and the angle bisectors in an equilateral triangle. The centroid is the intersection of the medians, which divide the triangle into six congruent triangles. Therefore, the orthocenter and the centroid coincide only when the triangle has three equal sides and angles. Created by Sal Khan.

## Want to join the conversation?

• Is there some type of mneumonic that could help memorizing all these triangle properties (incenter-circumcenter-centroid-orthocenter )
• ask there any special propertiespof the orthocenter
• He proves in an earlier video that any triangle can be made a medial triangle. The ortho center of the original triangle (which becomes the medial triangle) is also the circumcenter of the larger triangle.
• How do you find the orthocenter?
• The orthocenter is the point where all three altitudes of the triangle intersect. An altitude is a line which passes through a vertex of the triangle and is perpendicular to the opposite side. There are therefore three altitudes in a triangle.
(1 vote)
• Is an orthocenter the same thing as the circumcenter, and is the centroid the same thing as the incenter?
• Orthocenter - the point where the three altitudes of a triangle meet (given that the triangle is acute)
Circumcenter - the point where three perpendicular bisectors of a triangle meet
Centroid- the point where three medians of a triangle meet
Incenter- the point where the angle bisectors of a triangle meet

All are distinct, but like the example that Sal went through in the video, depending on the type of triangle, some can overlap.
• Are there any unique properties in Orthocenters?
• At , after he proved 3 pairs of congruent triangles by SAS, couldn't he have also used the RSH postulate to prove that all of them were congruent?
• Not as easily. The 3 hypotenuses that form the longer 2/3rds of each median line are not assumed to be equal at the beginning of the proof. Since we're trying to prove that it's an equilateral triangle we can't jump straight to using a property of an equilateral triangle at that point.
(1 vote)
• At I thought that it wasn't the same because they were different triangles the AFG is bigger than EFG what did I do wrong?
• When Sal talks about the angles being congruent, would all the angles have the same area and numbers?
(1 vote)
• If angles are congruent, they have the same measure in radians or degrees. I am not sure what you mean by 'area and numbers'