Pythagoras?Andrax said:
)tiny-tim said:Hi Andrax!
Just use the sine formula.
(mfb, i think it means the centroid of a weight AC at B and a weight AB at C
Ah, that makes sense.tiny-tim said:(mfb, i think it means the centroid of a weight AC at B and a weight AB at C
The centroid of a triangle is the point of intersection of the three medians of the triangle. A median is a line segment that connects a vertex of the triangle to the midpoint of the opposite side.
The centroid of a triangle can be calculated by finding the average of the x-coordinates and the average of the y-coordinates of the three vertices of the triangle. This will give the coordinates of the centroid (x̄, ȳ).
Proving the centroid of a triangle is important because it is a fundamental concept in geometry and is used in many geometric proofs and constructions. It also has practical applications in engineering and architecture.
The centroid is significant because it is the center of mass of the triangle. This means that if the triangle is cut out of a uniform material, the centroid is the point where it would balance perfectly on a pin. The centroid is also the center of the inscribed circle in a triangle.
The centroid of a triangle can be proved using various methods, such as using the properties of medians, vectors, or coordinates. One common method is by using the Triangle Midsegment Theorem, which states that the segment connecting the midpoints of two sides of a triangle is parallel to the third side and half its length. By using this theorem and the properties of parallel lines, the centroid can be proved.