Name:______________________________________
Bisectors, Medians, and Altitudes Intro Lab
Per:_____ Date:______________
1. CREATING A PERPENDICULAR BISECTOR. Construct CD . Then,
construct the midpoint of CD . Construct a perpendicular line through the
midpoint of CD . Name the intersection point E. Put point A on the
perpendicular line above CD , and put point B on the perpendicular line below
CD . AB is a perpendicular bisector.
a. Calculate the distances between all of the segments.
Which 3 sets of segments are congruent?
A
E
C
D
B
2. PERPENDICULAR BISECTORS and TRIANGLES. Since a triangle has 3
sides, it has 3 perpendicular bisectors. Create acute-scalene ABC . Using the
directions from #1, construct the perpendicular bisectors for each side of ABC .
Label the point where the 3 lines intersect X.
a. What is the name of the point where 3 perpendicular bisectors
meet? (use online resources to find the name)
B
X
C
A
b. Measure the distances of the triangle vertices to X. (AX,
BX, and CX)?
Is there a relationship? If so, what is it?
3. ANGLE BISECTORS and TRIANGLES. Create acute-scalene DEF . Since
the triangle has 3 angles, it will have 3 angle bisectors. Construct each of the 3
angle bisectors (highlight the 3 points in order, then select
E
CONSTRUCT… ANGLE BISECTOR). Label the point where
the 3 lines intersect P.
a. What is the name of the point where 3 angle bisectors
intersect? (use online resources to find the name)
P
D
b. HIDE all of the angle bisectors, but keep point P. Measure the distances
from P to each side of the triangle (highlight P and the segment,
MEASURE-DISTANCE). Is there a relationship? If so, what is it?
c. Click and drag point E. Does the intersection of the medians ever go
outside of the triangle?
F
4. MEDIANS and TRIANGLES. Create acute-scalene XYZ . Construct the
midpoint of each segment of the triangle. Label these points R, S, and T.
Connect the vertices of each angle to the midpoint on the side opposite the angle.
These segments are called medians. Label the intersection of
the medians W.
Y
S
a. What is the name of point W (the intersection of the
medians)? Use online resources to find the name.
R
W
X
T
b. There is a unique relationship with the medians and point W. Measure
SW and WZ . What is their relationship? Does the same thing happen
when you measure TW and WY ? RW and WX ?
c. Click and drag point Y. Does the intersection of the medians ever go
outside of the triangle?
5. ALTITUDES and TRIANGLES. Create acute-scalene JKL . Highlight
endpoint J and KL (side opposite J). Construct a perpendicular line. This line is
called an Altitude. Do this for the other sets of vertices and opposite segments (K
and JL , L and JK ). Label the intersection of the 3 altitudes F.
a. What is the name of the point where 3 altitudes intersect?
(use online resources to find the name)
K
J
F
L
b. Click point J and drag it until the triangle becomes
obtuse. Does the intersection point go outside of the
triangle?
c. Click point J and drag it until the triangle becomes right. What happens
to the intersection point of the altitudes?
BONUS: Create acute-scalene XYZ . On this triangle, create median XN and
altitude XL . What type of triangle is created when you drag points Y and Z, such that the
median and the altitude are the same? (TURN IN THIS IMAGE FOR BONUS
CREDIT)
Z