Theorems 5-8 through 5-11 relate to parallel lines and triangles. Theorem 5-8 states that if two lines are parallel, all points on one line are equidistant from the other. Theorem 5-9 says that if three parallel lines cut off congruent segments on one line, they will do so on any line that intersects them. Theorem 5-10 notes that a line through the midpoint of one side of a triangle, parallel to another side, will pass through the midpoint of the third side. Theorem 5-11, known as the Midsegment Theorem, specifies that the segment connecting the midpoints of two sides of a triangle is parallel to the third side and half its length.

1. Chapter 5
Quadrilaterals
5-3 Theorems Involving Parallel Lines

2. Theorem 5-8
If two lines are parallel, then all points on
one line are equidistant from the other
line.
A
C
B
D

3. Theorem 5-9
If three parallel lines cut off congruent segments
on one transversal, then they cut off congruent
segments on every transversal.

4. R
A
S
B
T
C

5. Theorem 5-10
A line that contains the midpoint of one side of
a triangle and is parallel to another side
passes through the midpoint of the third
side.

6. Theorem 5-11 Midsegment Theorem
The segment that joins the midpoints of two
sides of a triangle
(1) is parallel to the third side;
(2) is half as long as the third side.
A
M
B
N
C