Circumcenter:Where perpendicular bisectors cross.Incenter: Where angle bisectors meet inside. Centroid: Point where medians intersect, two-thirds from vertex to midpoint.
Orthocenter: Intersection of all altitudes, inside for acute, outside for obtuse, vertex for right-angled triangles.
Circumcenter:
1. Draw the triangle.
2. Find the perpendicular bisectors of any two sides of the triangle. The perpendicular bisectors are the lines that cut each side at right angles and are the same distance from the endpoints of the side.
3. The point where the two perpendicular bisectors intersect is the circumcenter.
Incenter:
1. Draw the triangle.
2. Draw the angle bisectors of any two angles of the triangle. The angle bisectors are the lines that divide each angle into two equal angles.
3. The point where the two angle bisectors intersect is the incenter.
Centroid:
1. Draw the triangle.
2. Find the midpoints of any two sides of the triangle. The midpoints are the points that are exactly halfway between the endpoints of the side.
3. Draw a line segment from one midpoint to the opposite vertex of the triangle. This line segment is called a median.
4. The point where the two medians intersect is the centroid.
Orthocenter:
1. Draw the triangle.
2. Draw the altitudes of the triangle. The altitudes are the lines that are perpendicular to a side of the triangle and pass through the opposite vertex.
3. The point where the three altitudes intersect is the orthocenter.
Here are some additional tips for finding these points:
You can use a compass and straightedge to draw the perpendicular bisectors and angle bisectors.
You can use a protractor to measure the angles of the triangle and then use those measurements to draw the angle bisectors.
The centroid is always two-thirds of the way from a vertex to the midpoint of the opposite side.
The orthocenter is often outside the triangle, but it can be inside the triangle, on a side of the triangle, or at a vertex of the triangle.