Math 2
Name________________________________
Lesson 4-5: Side Splitter & Midpoint Connector Theorems
Learning Goals:

I can use theorems, postulates, or definitions to prove theorems about triangles, including
the Side Splitter Theorem and the Midpoint Connector Theorem for Triangles
Part I – Side Splitter Theorem
1.
In the triangle to the right, DE || BC and the side lengths
are as marked. Prove that ADE ~ ABC
2.
If we look at ABC , we can see that DE splits sides AB and AC and is parallel to side BC .
AD
AE
Find the ratio
. Find the ratio
. What do you notice?
DB
EC
3.
Using the figure to the right, see if the relationship you
discovered in problem (2) is true for QRS .
Note that you should realize that QRS ~ QNO and that the
proof would follow the exact same logic as in problem (1).
4.
What you just discovered in problems (2) and (3) is what is called the Side Splitter Theorem.
Discuss in your groups and explain in your own words below what you think the Side Splitter
Theorem says.
5.
Write the Side Splitter Theorem down below (we will do this as a class). Later, in the extension
section of the practice problems, you can attempt a proof of the Side Splitter Theorem.
Solve for the given variable in the below problems. Use the Side Splitter Theorem when applicable.
1.
2.
3.
4.
Part II – Midpoint Connector Theorem
Triangle ABC has vertices A(0,  1), B(2, 5) and C ( 4, 1).
a. Find the coordinates of the midpoints of AB and BC.
Call these midpoints D and E, respectively and connect them.
D = _______ E = _______
b. Find the length of DE in Part a. Find the length of AC. How do the lengths compare?
DE  _______
Evaluate
AC  _______
Distance formula =
( x2  x1 )2  ( y2  y1 )2
DE

AC
What is the relationship between the length of the side of the triangle (AC) and the length of
the segment connecting the midpoints (DE)?
c. Find the slopes of DE and AC in Part a.
slope of DE =
slope of AC =
How do the slopes compare? What does this mean about the relationship between the
two segments?
d. Write the Midpoint Connector Theorem down below (we will do this as a class). Later, in the
extension section of the practice problems, you can attempt a proof of the Side Splitter Theorem.
The Midpoint Connector Theorem:
Part III: Practice
Solve the following problems for the given variables. Show your work. Your group will put one of
these problems on the board and should be able to explain the work needed to solve the problem.
1.
2.
3.
12
4.
Solve the following problems for the given variables. Show your work. Your group will put one of
these problems on the board and should be able to explain the work needed to solve the problem.
5.
6.
7.
8.
Solve the following problems for the given variables. Show your work. Your group will put one of
these problems on the board and should be able to explain the work needed to solve the problem.
9.
10. Find the coordinates of midpoints E and Z. Show that the slope of the line segment EZ is equal to
the slope of the line segment YT .