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# TEOREMA DE MENELAO

Matemática
by

## Mariela Villanueva

on 2 October 2013

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#### Transcript of TEOREMA DE MENELAO

TEOREMA DE
MENELAO
HIPOTESIS
DEMOSTRACIÓN
A
B
C
L
E
D
F
c
x
y
z
a.b.c

=

x.y.z
H
a
m
A
C
D
F
c
z
H
a
m
HBC
Teorema de THALES
m = c
a z
_ _
=>
m = ac
z
_
Teorema de THALES
HBC
B
C
L
E
D
F
x
y
H
m
m = y
x b
_ _
=>
m = xy
b
_
b
m = ac
z
_
m = xy
b
_
A
B
C
L
E
D
F
a
b
c
x
y
z
A
B
C
L
E
D
F
a
b
c
x
y
z
<< La recta secante a un , determina en dos de sus lados y en la prolongación del 3ro seis segmentos >>
a.
c
b.
=
x.
y.
z
Gracias
b
ac = xy
_ _
z b
a.b.c = x.y.z
Mariela Villanueva
Mariela Villanueva
Mariela Villanueva
LF // HC
Agosto
TESIS
_ _
Ejercicio
Una recta secante a un ABC,
trazada por el baricentro del triángulo,
corta a AB en P y a BC en Q.
Si BQ=10, QC=4, PB=9. Calcular AP.
A
B
C
G
p
Q
10
4
x
9
M
7
7
3
2a
a
9(2a)(3) = x(a)(10)
x= 5,4
Full transcript