Vickie Baier
Joanna Kosik
Intersection of Lines in Triangles
Medians
1. Construct triangle ABC.
2. Construct midpoint of each segment, label them D, E, and F.
3. Construct median from vertex A to the midpoint of the opposite side. Do the same from vertex
B to the midpoint of the opposite side. Label the intersection G.
4. Construct the third median from vertex C to the midpoint of the opposite side.
QI
What do you notice about the third median? Drag a vertex of the triangle. What do you observe for
a right, obtuse, acute, scalene, isosceles and equilateral triangle?
Angle Bisectors
1. Construct a new triangle HIJ.
2. Construct angle bisector for vertex H by highlighting points I, H & J (making sure that the angle
you want to bisect is in the middle). Do the same for vertex I. Label the intersection of the two
bisectors K.
3. Construct the third angle bisector for vertex J same as above.
Q2
What do you notice about the third angle bisector? Drag a vertex of the triangle. What do you
observe for a right, obtuse, acute, scalene, isosceles and equilateral triangle?
Altitude
1. Construct a new triangle LMN.
2. Construct a perpendicular line through vertex L to the side opposite. So the same for vertex M
to its side opposite. These lines are called the altitudes. Label the intersection of these lines O.
3. Construct a third altitude of vertex N.
Q3
What do you notice about the third altitude? Drag a vertex of the triangle. What do you observe for
a right, obtuse, acute, scalene, isosceles and equilateral triangle?
Perpendicular Bisector
1. Construct a new triangle PQR.
2. Construct midpoint of each segment, label them S, T & U.
3. Construct the perpendicular bisector through the midpoint of segments PQ and QR. Label the
intersection V.
4. Construct the third perpendicular bisector through the midpoint of the third segment.
Q4
What do you notice about the third perpendicular bisector? Drag a vertex of the triangle. What do
you observe for a right, obtuse, acute, scalene, isosceles and equilateral triangle?
Q5
The intersection of these lines meet in a point called_________________? (Match)
Medians
Orthocenter
Angle Bisector
Centroid
Altitude
Circumcenter
Perpendicular Bisector
Incenter