Give a fact about each of the following points associated
with a triangle:
a. incenter
b. circumcenter
c. orthocenter
d. centroid
This site will explain each one and help you memorize which one is which.
http://www.mathopenref.com/triangleincenter.html
a. The incenter of a triangle is the point where the angle bisectors of all three angles of the triangle intersect.
To find the incenter of a triangle, follow these steps:
1. Draw a triangle.
2. Bisect one angle of the triangle using a compass and a straightedge.
3. Repeat step 2 for the other two angles.
4. The three lines you draw will intersect at a single point. That point is the incenter of the triangle.
b. The circumcenter of a triangle is the point where the perpendicular bisectors of the sides of the triangle intersect.
To find the circumcenter of a triangle, follow these steps:
1. Draw a triangle.
2. Bisect one side of the triangle at a right angle using a compass and a straightedge.
3. Repeat step 2 for the other two sides of the triangle.
4. The three perpendicular bisectors will intersect at a single point. That point is the circumcenter of the triangle.
c. The orthocenter of a triangle is the point of intersection of the altitudes of the triangle.
To find the orthocenter of a triangle, follow these steps:
1. Draw a triangle.
2. Construct the altitude of one side by drawing a perpendicular line from the opposite vertex to that side.
3. Repeat step 2 for the other two sides of the triangle.
4. The three altitudes will intersect at a single point. That point is the orthocenter of the triangle.
d. The centroid of a triangle is the point of intersection of the medians of the triangle.
To find the centroid of a triangle, follow these steps:
1. Draw a triangle.
2. Construct the median of one side by drawing a line from the midpoint of that side to the opposite vertex.
3. Repeat step 2 for the other two sides of the triangle.
4. The three medians will intersect at a single point. That point is the centroid of the triangle.
These points associated with a triangle have unique properties and play important roles in various geometric calculations and constructions.