Triangulos diapositivas 2
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PROF. LIC . PATRICIA PEREZ GARCÍA.
GRADO: TERCERO SEC
Colegio Particular
"Santa María Reina"
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A
B
C
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A
B
C
b
c a
El perímetro de un triángulo es la suma de
las longitudes de sus tres lados y se le
representa por 2P.
Perímetro=2P= a + b + c
a + b + c
El semiperímetro , se representa por P.
Semiperímetro = Perímetro
2
P= a + b + c
2
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A
B
CY Z
X
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B
A
C
x
y
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A
B
C
HIPÓTESIS:
, , : medidas de los
ángulos exteriores.
, , : medida de los ángulos
interiores.
TESIS:
+ + =360°
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A
B
C
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A
B
C
a < b + c
a > b – c
b – c < a < b + c
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A
B
C
X = 90° +
2
X
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X
A
B
C
EX = 90 -
2
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X
A
B
C
E
X =
2
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X
φ
A
B
C
ED
X = 180° - φ
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A
B C
θ
Φ
COROLARIOS
1. Los ángulos agudos de un triángulo rectángulo son
complementarios .
Φ + θ = 90°
- θΦ = 90°
ΦΘ = 90° -
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45°
45°
2. La medida de los ángulos agudos de un triángulo
rectángulo isósceles miden 45° cada uno.
A
B
C
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3. N i n g ú n t r i á n g u l o p u e d e
t e n e r m á s d e u n á n g u l o
r e c t o .
4. N i n g ú n t r i á n g u l o p u e d e
t e n e r m á s d e u n á n g u l o
o b t u s o .
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5. La medida de un ángulo exterior es mayor que
cualquiera de las medidas de los ángulos
interiores que no le son adyacentes.
Φ
y
z
Φ > Z
Φ > y
A
B
C
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1.
3.
2.
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TEOREMA DE LAS BISECTTRICES INTERIORES
TEOREMA DE LAS BISECTTRICES EXTERIORES
TEOREMA DE LAS BISECTTRICES INTERIOR Y UNA BISECTRIZ
EXTERIOR
TEOREMA DE 2 ALTURAS TEOREMA DEL CUADRILÁTERO NO
CONVEXO
TEOREMA DE LA ALTURA Y LA BISECTRIZ INTERIOR
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A)50º b)60º c)70º d) 80º e)30º
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A)50º
b)70º
c)20º
d) 90º
e)30º
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a)45º
b)20º
c)40º
d)55º
e)45º
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A)25º b)20º c)46º d)40º e)60º
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