A GEOMETRIA NO 9º ANO NO ENSINO FUNDAMENTAL
Autor: MATEMATICA 09/13 | Publicado: 2011-12-14T12:01:00-08:00

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FACULDADE DA MATA SUL – FAMASUL

CURSO DE LICENCIATURA EM MATEMÁTICA



A GEOMETRIA NO 9º ANO NO ENSINO
FUNDAMENTAL

José Robson Nascimento de Oliveira

José Valério Floriano Silva

Naedja Claudia Nascimento da Mata

Projeto de
intervenção pedagógica apresentado para a Disciplina de Prática Pedagógica no 5º
período do curso de Licenciatura de Matemática da Faculdade da Mata Sul –
FAMASUL



Professor: Andréia Soraia

Palmares/11

SUMÁRIO

Introdução......................................................................................................................03

Problemática..................................................................................................................04

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Público
alvo.......................................................................................4.1

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Tempo
Estimado...............................................................................4.2

Conteúdo..........................................................................................4.3

Material
utilizado..............................................................................4.4

Justificativa....................................................................................................................05

Objetivo Geral e Especifico..........................................................................................06

Desenvolvimento............................................................................................................07

Metodologia....................................................................................................................08

Conclusão.......................................................................................................................11

Referência......................................................................................................................12

INTRODUÇÃO



O ensino da
geometria na escola, não ocorre com freqüência, por que muitos Educadores não se
aprofundam nesta área por ser um assunto complexo, causando assim uma
deficiência no aprendizado do Educando.

&nbsp;A identificação do problema leva a uma
capacitação e isto leva a resolução do problema, tudo para dar um bom aprendizado
ao Educando, para que no futuro, já no ensino superior, ter uma base sólida.

Problemática: A
Geometria no 9º ano no Ensino Fundamental 



&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;A ausência do ensino da Geometria no nono ano
do ensino fundamental, passou a ser um grande problema nas Escolas, pois quando
o Educando se depara com esta problemática na série final ele apresenta um mau
desempenho causando uma dificuldade na sua aprendizagem.

Portanto, para
que este problema venha a ser sanado o professor tem que desenvolver métodos de
aprendizagem procurando caminhos que venha a facilitar e aguçar a curiosidade
do Educando para este assunto, causando assim algo que desfrute prazer e
conhecimento e não um roteiro de quebra-cabeças.

4.1 Público alvo: Educando do 9º ano do Ensino Fundamental

4.2 Tempo Estimado: 06 aulas

4.3 Conteúdo:

Explanação
     do Os Elemento de Euclides, escrito em 12
     volumes.
Formas
     e desenhos Geométricos o que são?
Explanação
     sobre Ponto.
Explanação
     sobre Reta.
Explanação
     sobre Plano.
Explanação
     sobre Arestas
Explanação
     sobre Face
Explanação
     sobre Vértice


4.4&nbsp; Material Utilizado:

Régua
Esquadro
Compasso
Transferidor
Lápis
Borracha
Caderno
     de Desenho
Tesouras
Papelão
Isopor
Quadro
     Branco
Lápis
     para o quadro branco
Paralelepípedo
     
Geoplano


Objetivo Geral: 

·&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
Despertar no Educando a importância da Geometria
e a praticidade em todas as áreas, especificamente em matemática causando assim
uma mobilização do educando para um ensino/aprendizagem seguro e com capacidade
de construir caminhos que facilite a resolução das mais diversas
situações-problema na sua vida.

Objetivo Específico: 

Analisar a visão do educando com relação á
     importância da Geometria na construção do conhecimento.
Realizar um debate sobre formas geométricas e onde
     elas são encontradas. 
Mostrar formas geométricas sólidas como aula
     prática
Desenvolver o conhecimento e o interesse pela
     Geometria.


JUSTIFICATIVA

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; A
Geometria tem por objetivo estudar as formas de objetos ou figuras e
estabelecer relações entre as medidas de suas partes e entre figuras
diferentes, para que identifiquemos e elaboremos resultados para diversos
problemas que nos deparamos no nosso cotidiano, pois se&nbsp; que observarmos ao nosso redor encontramos em
toda parte a Geometria, ou seja, vivemos dentro das medidas e figuras
geométricas. 

DESENVOLVIMENTO

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; O
pensador grego que mais se destacou na Geometria foi EUCLIDES (séc. III a.c),
ele reuniu as descobertas já feitas, complementou-as e as organizou de forma
sistemática em uma obra chamada os
elemento, escrita em 12 (doze) volumes, estas obras foram tão importantes
que até nos dias de hoje em pleno séc. 21, em meios de vários estudiosos,
EUCLIDES ainda é conhecido “O pai da Geometria”.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Vamos
agora idealizar um paralelepípedos observando as característica de um baú
retangular, cada um de seus cantos verticais da á idéia de ponto, cada uma de
suas 12 (doze) arestas dá idéia de “pedaços de retas”, agora se pudéssemos
prolongar cada aresta indefinidamente teríamos uma reta.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Cada
uma de suas 06 (seis) faces da idéia de “pedaço de plano”, agora se pudesse
ampliar cada face indefinidamente em todas as direções, teria um plano. 

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;O Geoplano é formado por uma placa de madeira
quadriculada com pregos nos vértices de cada quadrinho, as cabeças dos pregos
dão idéias de pontos, pode-se dizer que o ponto não tem tamanho, pois não é
possível medi-lo, então, temos apenas uma representação. Os pontos são
indicados por letras maiúsculas e as retas são por letras minúsculas. Veja na
figura 01 abaixo, as representações de alguns pontos e retas. 

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Toda
reta é um conjunto em que os elementos são pontos.



Fig. 01

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Ponto A

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; A



&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; reta

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;b&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Ponto E&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; B





&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
Ponto C

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; C

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;reta

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; a

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Ponto D

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; D





&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
reta c

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; E

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Ponto B



Vamos ver mais
um exemplo de que a mais simples forma Geométrica está no nosso dia a dia.

·&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
Em uma quadra de esporte; o piso permite formar
a idéia de plano; á linha que divide os lados ajuda a dar a idéia de reta e o
centro dá a idéia de ponto, conforme a figura 02 abaixo. 

Fig. 02





 

  
  
  
  
  
  
 

  
  
  
 

  
  
  
  
  
 

  
 




















&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; A
Geometria é a parte da Matemática que está voltada á formas, sendo que os
personagens principais de um curso Geométrico são as formas e figuras, onde é
através do estudo dessa disciplina que construímos com precisão figuras
geométricas utilizando habilidade três instrumentos a régua, o par de esquadros
e o compasso.

Iremos agora
falar sobre dois segmentos congruentes, o qual significa duas retas do mesmo tamanho
como mostra o a figura 02



Fig. 03

A &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;B&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; AB
e CD tem o mesmo tamanho, portanto AB e &nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; CD são
congruentes. Lê-se o segmento AB é 

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; D&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;  congruente ao segmento CD.



&nbsp;&nbsp;&nbsp;&nbsp; 

&nbsp;&nbsp;&nbsp;&nbsp; C

&nbsp;&nbsp;&nbsp; 

Medir um segmento de reta AB
significa determinar quantas vezes um segmento unitário padrão (metros,
centímetros, milímetros e etc.) cabe no segmento AB, veja o segmento AB em
centímetros na figura 07.

Fig. 04 

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; A&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp; B&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; AB
mede 6 cm





&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Também
é importante na Geometria o uso do par de esquadros, instrumentos que permite
desenhar retas paralelas e perpendiculares. Existem dois tipos de esquadros o
de 45º e de 30º por 60º grau, esses graus chamasse ângulos, o qual é a união de
duas semirretas de mesma origem.

&nbsp;Uma boa maneira de comparar duas grandezas,
como o comprimento de dois segmentos, é calcular o quociente entre suas medidas,
podemos então definir o que é razão entre dois segmentos, na verdade, estamos
falando da razão de suas medidas, tomadas na mesma unidade.

Paralelas
igualmente espaçadas; percebemos que as retas a, b, c, d e “e” são paralelas
entre si. Dizemos, então, que elas são retas paralelas igualmente espaçadas,
conforme mostra a figura 03

Fig. 05&nbsp;&nbsp; &nbsp;



&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; a



&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; b

c



d

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; e

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Semelhança
(formas e tamanhos), durante varias gerações uma obra foi usada como manual
para o ensino da geometria devido ao rigor matemático com que tratava o
assunto, pois bem, hoje trabalhamos em cima dos ensinamentos do “PAI DA
GEOMETRIA” para que seu rigor matemático nos mostre o esclarecimento de um
curioso paradoxo geométrico. O problema em questão refere-se a uma divisão de
um terreno ABCDEFG em quatro lotes (ABG, BCD, EDF e GBDF), segundo nosso
conhecimento geométrico sobre o calculo da área de um triangulo (base
multiplicada pela altura e dividida por dois) e da área de um retângulo (base
multiplicada pela altura), sabemos as áreas S1, S2, S3 e S4 de cada terreno
serão respectivamente iguais a 2.000
 m², 1.5000
 m², 2.000
 m² e 4.800
 m², perfazendo 10.300 m² de área total no terreno por outro
lado, se quiséssemos calcular a área total do terreno, admitindo sua forma de
um triângulo de base AE, medindo 160 metros e altura igual a 130 metros, pela formula
da área de um triângulo, concluiremos que o terreno tem área total de 10.400 m² (ganhamos 100 m² em relação ao calculo
anterior) como explicamos esse paradoxo digno de causar calafrios até ao “PAI
DA GEOMETRIA” ?.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Note
que os segmentos AG e BD são paralelos, mas os ângulos BÂG e CBD não são
congruentes (sua tangente são iguais a 8/5 e 5/3 respectivamente), se esses
ângulos não são congruentes, segue que os A, B e C não estão alinhados,
portanto ABCDE não é um triângulo, apesar de isto ser imperceptível
visualmente, ocorrendo que o calculo correto da área total do terreno deve ser
feito pela soma da área de cada um dos quatros lotes. O ganho de 100 m² de um calcula em
relação a outro se deve á diferença entre a área do triângulo ACE (assumida
equivocadamente como a área do terreno) e a área do polígono côncavo ABCDE
(área do terreno).

Fig. 06

 

  
  


 






























METODOLOGIA

O projeto
propõe um desenvolvimento teórico e prático relacionando o cotidiano com o
ensino/aprendizagem do Educando da seguinte maneira:

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 



1.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Etapa:

·&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
Nesta etapa realizarei uma explanação
rápida e básica sobre a História da Geometria. 

2.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Etapa:

·&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
Será
mostrada uma forma geométrica sólida encontrada no nosso dia a dia como exemplo
e logo após uma explicação das suas características.

3.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Etapa:

·&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
Será apresentado ao educando materiais
para desenhos geométricos e ensinado como usar-los. 

4.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Etapa:

·&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
Nesta etapa realizarei uma
explanação mais profunda sobre as características de uma figura geométrica,
conceituando pontos, retas e planos.

5.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
Etapa: 

·&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
Nesta etapa aplicaremos na prática o
que foi aprendido, utilizando materiais para confecção de figuras ou objetos
geométricos.

Produto final:


·&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
Construção de figura e objetos
geométricos com aproveitamento do ensino/aprendizagem.



Avaliação:

·&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
Os alunos serão avaliados através de
uma prova prática com utilização do material para desenho geométrico (compasso,
esquadro, régua e transferidor), onde eles terão de construir um objeto
geométrico solido e um desenho geométrico.

CONCLUSÃO

Ao concluímos
este projeto, tivemos a possibilidade de ver como o educando absolveu o
ensino/aprendizagem da Geometria, porém para que eles tivessem um bom
desenvolvimento foi preciso um ensino prático e ter uma visão ampla do assunto,
possibilitando uma base sólida quando estiverem no ensino superior.

REFERÊNCIA

DANTE, Luiz Roberto. Tudo é Matemática, Editora
     Ática, 2002 - 9º (nono) ano 




REVISTA NOVA ESCOLA/ABRIL 2011




SITE SÓ MATEMÁTICA – www.sómatemática.com