Proportionality Theorems

1
Proportionality Theorems
2
Theorem 60-1Triangle Proportionality theorem

• If a line parallel to one side of a triangle
  intersects the other 2 sides, it divides those
  sides proportionally
• AD AE
• DB EC

3
Using Proportionality to find unknowns

• Find the length of line segment RT
• QS RT
• SP TP

4
Find x
X3
X1
10
5
5
Theorem 60-2Converse of Triangle Proportionality
theorem

• If a line divides 2 sides of a triangle
  proportionally, then it is parallel to the 3rd
  side
• AD AE then DE is parallel to BC
• DB EC

6
Proving lines parallel

• Is ST parallel to PR?
• PS RT
• SQ TQ

S
P
3
8
Q
7
T
R
2
7
Theorem 60-3

• If parallel lines intersect transversals, then
  they divide the transversals proportionally
• PQ JK
• QR KL

8

• If parallel lines divide a transversal into
  congruent segments, then the segments are in a
  11 ratio. By theorem 60-3, any other transversal
  cut by the same parallel lines will be divided
  into segments that also have a 11 ratio, so they
  will also be congruent.

3
3
9
Theorem 60-4

• If parallel lines cut congruent segments on one
  transversal, then they cut congruent segments on
  all transversals.
• IF AB BC, then DE EF

10
Finding segment lengths with intersecting
transversals

• Find the length of AB

4
X3
4
3x-1
11
practice

• Determine whether AD, BE, and CF are parallel
  when x 3

x
4x-1
14
y
5x-3
14
z
12
Find the length of EB

• ED is parallel to BC

B
E
4
C
D
A
6
10
13
Find the length of PQ

• PR is parallel to AB

Q
x
A
2x-1
P
5
B
3
R
14
practice

• Find the length of AD

3
B
4
A
2
15
practice

• Are the lines parallel ?
• Y 9, X 9.75,C 12, E 13

does