CHAPTER 16. GEOMETRY 16.4
16.4 Triangle Geometry.
Proportion EMBCJ
Two line segments are divided in the same proportion if the ratiosbetween their parts areequal.
AB
BC
=
x
y=
kx
ky=
DE
EF
∴ the line segments are in the same proportionA
B
C
D
E
F
xykx
kyIf the line segments areproportional, the following also hold:
1.CBAC=FEDF
2. AC. F E = CB. DF
3.ABBC=DEFEandBCAB=DEFE4.ABAC=DEDFandACAB=DFDEProportionality of triangles
Triangles with equal heights have areas which are in the same proportion to each other as the bases of
the triangles.
h 1 = h 2∴
area�ABC
area�DEF=
1
2 BC× h^1
1
2 EF× h^2=
BC
EF
A
B C
D
E F
h 1h 2