16.4 CHAPTER 16. GEOMETRY
- A special case of this happens when the basesof the triangles are equal:
Triangles with equal bases between the same parallel lines have the same area.
area�ABC =1
2
. h. BC = area�DBC
A
B C
D
h- Triangles on the same side of the same base, with equal areas, lie between parallel lines.
If area�ABC = area�BDCthen AD� BCA
B C
D
Theorem 1. Proportion Theorem: Aline drawn parallel to one side of a triangle divides the other two
sides proportionally.
A
A A
B C B
B
C
C
D
D
D
E
E
E
h 1
h 2Given:�ABC with line DE� BC
R.T.P.:
AD
DB
=
AE
EC
Proof: Draw h 1 from E perpendicular to AD, and h 2 from D perpendicular to AE.