1) Draw a scalene triangle. Find (construct) the incenter, circumcenter, centroid, and orthocenter. What seems to be true
about these points? List these points in your response.
2) True or false
a) The orthocenter of a right triangle is located on the hypotenuse.
b) The circumcenter of a scalen triangle lies outside of the triangle.
3) Ryan wants to balance a triangle on the tip of his pencil, which point of concurrency should he find.
about these points? List these points in your response.
2) True or false
a) The orthocenter of a right triangle is located on the hypotenuse.
b) The circumcenter of a scalen triangle lies outside of the triangle.
3) Ryan wants to balance a triangle on the tip of his pencil, which point of concurrency should he find.
6) A triangle has vertices at \(H(4, 5)\), \(V(22, –3)\), and \(P(–18, –5)\).
a) Find the coordinates of the centroid.
b) Find the coordinates of the centroid of triangle form by joining the midpoints of \(\triangle HVP\).
7) The centroid of a triangle is \((6, 9)\) and two of the vertices of the triangle are \((1, 6\)) and \((12, 8)\). Find the third
vertex.
8) The centroid of a \(\triangle OLI\) is \((-11, 8)\). Find coordinates for \(O\), \(L\), and \(I\).
9) Given \(\triangle SAR\) with \(S(0, 7)\), \(A(0, 0)\) and \(R(24, 0)\).
a) Find the coordinates of the incenter.
b) Find the coordinates of the circumcenter.
10) “All triangles can be inscribed in a circle.” Prove this statement using the material in the learning target.
Solution Bank
a) Find the coordinates of the centroid.
b) Find the coordinates of the centroid of triangle form by joining the midpoints of \(\triangle HVP\).
7) The centroid of a triangle is \((6, 9)\) and two of the vertices of the triangle are \((1, 6\)) and \((12, 8)\). Find the third
vertex.
8) The centroid of a \(\triangle OLI\) is \((-11, 8)\). Find coordinates for \(O\), \(L\), and \(I\).
9) Given \(\triangle SAR\) with \(S(0, 7)\), \(A(0, 0)\) and \(R(24, 0)\).
a) Find the coordinates of the incenter.
b) Find the coordinates of the circumcenter.
10) “All triangles can be inscribed in a circle.” Prove this statement using the material in the learning target.
Solution Bank