What is the centroid of a triangle?
Altitudes, Medians, & Centers

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Mathematics
•
10th Grade
•
Hard
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1.
FLASHCARD QUESTION
Front
Back
The centroid is the point where the three medians of a triangle intersect. It is also the center of mass of the triangle.
2.
FLASHCARD QUESTION
Front
How do you find the centroid of a triangle given its vertices?
Back
To find the centroid (G) of a triangle with vertices A(x1, y1), B(x2, y2), and C(x3, y3), use the formula: G = ( (x1 + x2 + x3)/3 , (y1 + y2 + y3)/3 ).
3.
FLASHCARD QUESTION
Front
What are medians in a triangle?
Back
Medians are line segments that connect a vertex of the triangle to the midpoint of the opposite side.
4.
FLASHCARD QUESTION
Front
What is the relationship between the centroid and the medians?
Back
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.
5.
FLASHCARD QUESTION
Front
What is an altitude in a triangle?
Back
An altitude is a perpendicular segment from a vertex to the line containing the opposite side.
6.
FLASHCARD QUESTION
Front
Where do the altitudes of a triangle intersect?
Back
The altitudes of a triangle intersect at a point called the orthocenter.
7.
FLASHCARD QUESTION
Front
What is the orthocenter of a triangle?
Back
The orthocenter is the point where all three altitudes of a triangle meet.
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