Math 2
Name________________________________
Lesson 4-5: Side Splitter & Midpoint Connector Theorems Date ____________________________
Learning Goals:

I can use theorems, postulates, or definitions to prove theorems about triangles, including:
a. A line parallel to one side of a triangle divides the other two proportionally;
b. If a line divides two sides of a triangle proportionally, then it is parallel to the third side;
Part I – Side Splitter Theorem
The Side Splitter Theorem states that a line parallel to one side of a triangle divides the other two
proportionally.
w x
Given: DE BC
Prove: 
y z
1.
Solve for x:
2. Solve for x:
OVER 
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?
The Midpoint Connector Theorem:
Part III: Solve the following problems. Show your work.
1. Solve for x and y.
Solve each of the following for x and y.
2.
3.
12
4.
5.
OVER 
6.
7.
8.
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 .