Area Method Geometry Worksheet With Answers
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1450 MATHCOUNTS LECTURES
(34) AREA METHOD
BASIC KNOWLEDGE
Theorem 1: The ratio of the areas of any two triangles is:
1
AB
H
S
AB
H
2
ABC
1
S
A
B
H
A
B
H
A
B
C
1
1
1
1
1
1
1
1
1
2
Theorem 2: If two triangles have the same base, the ratio of the areas is the ratio of the
heights.
S
H
ABD
S
h
ABC
Theorem 3: If two triangles have the height, the ratio of the areas is the ratio of the bases.
S
AB
S
AB
S
AD
ABC
ABC
ADC
;
;
.
S
AD
S
DB
S
DB
ADC
DBC
BDC
Theorem 4(a): If AB//CD, then S
= S
and S
= S
ABC
ABD
AED
BEC
(Same base and same height).
4(b): If S
= S
, then AB//CD.
AED
BEC
227
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