1. Proportionality Theorems

2. Theorem 60-1 Triangle 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
X+1
X+3 10 5

5. Theorem 60-2 Converse 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 P 3 S 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 1:1 ratio. By theorem 60-3, any other transversal cut by the same parallel lines will be divided into segments that also have a 1:1 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
X+3 4
3x-1 4

11. practice Determine whether AD, BE, and CF are parallel when x = 3 x14 y
5x-3 14 z

12. Find the length of EB
ED is parallel to BC B E 4 C A D 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