Name: _____________________________ Date: ______________________ Block#: ______________
Geometry CP Points of concurrence in triangles
I.
Medians
Obtuse triangle
Acute Triangle
Right Triangle
II.
Perpendicular Bisector
Obtuse triangle
Acute Triangle
Right Triangle
III.
Altitude
Obtuse triangle
Acute Triangle
Right Triangle
IV.
Angle Bisector
Obtuse triangle
Acute Triangle
Right Triangle
Read over pages 176-184, then complete the following directions and answer any questions.
I.
Median
1) The median of a triangle is drawn from the midpoint of the side to the opposite vertex.
2) Label each triangle ABC.
3) On the page labeled ‘median ’, draw medians from the midpoint of the side of each triangle to
the opposite vertex. Label the points where the medians DE and F so that when you connect the
points to the vertices you have medians AD, BE and CF.
4) Mark the new congruent parts of the sides properly with hash marks.
Mark the point of concurrence of the medians G. What is this point called?
Repeat this procedure for each triangle on that page. Is the point of concurrence within the
triangle each time?
II.
Perpendicular bisector
1) The perpendicular bisector of a triangle is drawn at a ninety degree angle to each side from its
midpoint. Label each triangle ABC then draw the three pb’s on the page marked ‘perpendicular
bisectors’ and label the three points on the sides DEF so you have lines AD, BE and DF.
2) Do these new lines go through the vertex?
3) Mark the point of concurrence G. What is the name of the point of concurrence for these lines?
4) Is the point of concurrence inside the triangle?
5) Repeat the procedure for all the triangles on the page and answer the questions for each one.
III.
altitude
1) The altitude of a triangle is drawn at a ninety degree angle to the side it touches to the opposite
vertex. Label each triangle ABC then draw the three altitudes on the page marked ‘Altitudes’
and label the three points on the sides DEF so you have lines AD, BE and DF.
2) Mark the point of concurrence G. What is the name of the point of concurrence for these lines?
3) Is the point of concurrence inside the triangle?
4) Repeat the procedure for all the triangles on the page and answer the questions for each one.
IV.
Angle bisector
1) The angle bisector is drawn from the vertex to the opposite side, using the protractor to
measure and bisect each angle first. Label each triangle ABC then draw the three
altitudes on the page marked ‘Angle bisector’ and label the three points on the sides
DEF so you have lines AD, BE and DF.
2) Mark the congruent angles with hash marks.
3) Mark the point of concurrence G. What is the name of the point of concurrence for
these lines?
4) Is the point of concurrence inside the triangle?
5) Repeat the procedure for all the triangles on the page and answer the questions for
each one.
Go to page 183-185 and compete investigation #2 (center of gravity). Answer the
questions here. This packet must be completed and handed in before the end of today’s
class. It is a quiz grade. You may work with your group but must hand in your own
packet. Good luck!