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Matemática
Geometria Plana
Quadriláteros
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Katharina Martins
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Trapézio
Escaleno
: os lados
adjacentes
não são
congruentes.
Trapézio Isósceles
: os lados
adjacentes
são
congruentes.
Trapézio Retângulo
: um dos lados adjacentes forma
dois
ângulos
retos
com as bases.
A
+
A +
A
+
D
=
D =
D
=
B
+
B +
B
+
C
=
C =
C
=
180
°
180°
180°
A soma dos ângulos internos
opostos
de um
trapézio
é igual a 180°.
A
base
média
de um
trapézio
é
M
N
=
MN =
MN
=
a
+
b
2
\frac{a+b}{2}
2
a
+
b
A base que intercepta o encontro das diagonais de um trapézio é dada por:
P
R
=
PR =
PR
=
2
a
b
a
+
b
\frac{2ab}{a+b}
a
+
b
2
ab
A área de um trapézio é calculada através da fórmula:
A
ˊ
rea
=
\text{Área} =
A
ˊ
rea
=
(
a
+
b
)
h
2
\frac{(a+b)h}{2}
2
(
a
+
b
)
h
, onde h é a altura do trapézio.
Os ângulos opostos em um paralelogramo são
congruentes.
Os lados opostos em um paralelogramo são
congruentes.
As diagonais de um paralelogramo se interceptam nos respectivos
pontos médios.
As diagonais de um losango são
bissetrizes
e
mediatrizes.
O
centroide
de um losango está no ponto de intersecção das diagonais.
Um quadrilátero convexo é
inscritível
se, e somente se, seus ângulos opostos são
suplementares
(180°).
Um quadrilátero é
circunscritível
se, e somente se, a soma dos seus lados opostos forem
iguais.
Se o quadrilátero é
inscritível
, então o produto de suas
diagonais
é igual à soma dos produtos dos lados
opostos.
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