semelhança de triângulos

1. ATIVIDADE PROPOSTA SOBRE
SEMELHANÇA DE TRIÂNGULOS

2. Um prédio projeta no solo uma sombra de 30 m de extensão
no mesmo instante em que uma pessoa de 1,80 m projeta uma
sombra de 2,0 m. Pode-se afirmar que a altura do prédio vale
a) 27 m
b) 30 m
c) 33 m
d) 36 m
e) 40 m

3. Renata quer calcular a altura da sua caixa d’água. Para isso, durante o
dia, ela observou a sombra de um pedaço de madeira reto ao lado da
caixa d’água e mediu o comprimento da sombra, que era de 0,6 metro.
Já a sombra da caixa d’água era de 3,40 metros, conforme a imagem a
seguir. Sabendo que a altura do pedaço de madeira era de 1,4 metro,
então a altura da caixa d’água é de:
A) 9,1 metros.
B) 8,5 metros.
C) 8,2 metros.
D) 8,0 metros.
E) 7,9 metros.

4. Para descobrir a altura de um prédio, Luiz mediu a
sombra do edifício e, em seguida, mediu sua própria
sombra. A sombra do prédio media 7 metros, e a de
Luiz, que tem 1,6 metros de altura, media 0,2 metros.
Qual a altura desse prédio?
a) 50 metros
b) 56 metros
c) 60 metros
d) 66 metros
e) 70 metros

5. Qual o valor de x nos triângulos a seguir?
a) 48 cm
b) 49 cm
c) 50 cm
d) 24 cm
e) 20 cm

6. Na imagem a seguir, é possível perceber dois triângulos que
compartilham parte de dois lados. Sabendo que os segmentos
BA e DE são paralelos, qual a medida de x?
a) 210 m
b) 220 m
c) 230 m
d) 240 m
e) 250 m

7. Dado o triângulo a seguir e sabendo que o
segmento DE é paralelo à base CB e que AC mede
10 cm, AD mede 4 cm e AE é igual a 5 cm, então
podemos afirmar que o segmento BE mede:
A) 11 cm.
B) 10,5 cm.
C) 9,5 cm.
D) 8,0 cm.
E) 7,5 cm.

8. Analisando os triângulos a seguir, sabendo que AB
é paralelo a DC, então podemos afirmar que x é
aproximadamente:
A) 9,2
B) 9,6
C) 10, 5
D) 10,8
E) 11,0

9. Existem alguns procedimentos que podem ser usados para
descobrir se dois triângulos são semelhantes sem ter de
analisar a proporcionalidade de todos os lados e, ao mesmo
tempo, as medidas de todos os ângulos desses triângulos. A
respeito desses casos, assinale a alternativa correta:
a) Para que dois triângulos sejam semelhantes, basta que eles
tenham três ângulos correspondentes congruentes.
b) Para que dois triângulos sejam semelhantes, basta que eles
tenham dois lados proporcionais e um ângulo congruente, em
qualquer ordem.
c) Para que dois triângulos sejam semelhantes, basta que eles
tenham os três lados correspondentes com medidas
proporcionais.
d) Dois triângulos que possuem dois lados correspondentes
proporcionais não serão semelhantes em qualquer hipótese.
e) Dois triângulos que possuem apenas dois ângulos
correspondentes congruentes não podem ser considerados
semelhantes.

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