NAME
5-2
DATE
PERIOD
Enrichment
Constructing Centroids and Orthocenters
The three medians of a triangle intersect at a single point called the centroid.
You can use a straightedge and compass to find the centroid of a triangle.
6
1. With a straightedge and compass, construct the
centroid for STU by following the steps below.
Step 1 Locate the midpoints of sides TU and SU.
Label the midpoints A and B respectively.
Step 2 Draw the segments SA and TB. Use the
letter H to label their point of intersection,
which is the centroid of STU.
Construct the centroid of each triangle.
2.
5
4
6
#
"
)
5
4
3.
The three altitudes of a triangle meet in a single point called the orthocenter of the triangle.
Step 1 Extend segments CD and DE past point
D long enough to meet perpendiculars
from E and C as shown.
Step 2 Construct the perpendicular from point C
to the line DE and label the point of
intersection X. Likewise, label the point of
intersection of line CD with the perpendicular
from E as point Z. In this case
both X and Z lie outside CDE.
Step 3 Label O the point where perpendiculars
and EZ
intersect. This is the
CX
orthocenter of CDE.
$
%
&
%
&
$
9
0
;
Construct the orthocenter of each triangle.
5.
Chapter 5
6.
16
Glencoe Geometry
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
4. Follow the steps below to construct the orthocenter
of CDE using a straightedge and compass.