Matières

Maths

Géométrie

Dans les triangles

Théorème de thalès

Programme Maths 3ème 2024: Exercices Corrigés & Théorème de Thalès

Name: Knowunity
Brand: Knowunity

Voir

Programme Maths 3ème 2024: Exercices Corrigés & Théorème de Thalès

Julien

@revaliiuwu

22 Abonnés

Suivre

The overall summary and page-by-page summaries for the provided PDF transcript are as follows:

Mathematics concepts for 3ème level, covering geometry theorems, ratios, data analysis, and trigonometry. Key topics include Pythagoras' theorem, Thales' theorem, ratios, data management, and trigonometric functions.

• Geometry: Pythagoras' theorem and its converse, Thales' theorem
• Numbers: Ratios and proportions
• Data analysis: Mean, median, quartiles, and range
• Trigonometry: Basic trigonometric ratios and inverse trigonometric functions
• Equations: Solving linear equations

19/04/2022

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Voir

Page 1: Geometric Theorems

This page focuses on fundamental geometric theorems crucial for maths 3ème students. It covers the Pythagoras' theorem, its converse, and Thales' theorem.

The Pythagoras' theorem is presented for right-angled triangles, stating that the square of the hypotenuse equals the sum of squares of the other two sides.

Definition: In a right-angled triangle, BC² = AC² + AB², where BC is the hypotenuse.

The converse of Pythagoras' theorem is also explained, which is used to determine if a triangle is right-angled.

Example: For triangle NYC, if NC² = NY² + YC² (3² + 4² = 5²), then NYC is a right-angled triangle.

Thales' theorem is introduced for similar triangles, showing the proportionality of corresponding sides.

Highlight: Thales' theorem states that AM/AB = MN/BC = AN/AC for similar triangles AMN and ABC.

The page concludes with a note on using cross multiplication to find missing values in Thales' theorem applications.

Vocabulary: Théorème de Thalès (Thales' theorem), Théorème de Pythagore (Pythagoras' theorem), hypotenuse, right-angled triangle.

Voir

Page 2: Ratios and Data Analysis

This page delves into ratios and data analysis techniques, essential components of the Programme maths 3ème.

The concept of ratios is explained, showing how to express relationships between numbers and divide quantities proportionally.

Example: To share 240€ between two people in the ratio 2:3, divide 240 by (2+3)=5, then multiply by respective ratio parts: 48x2=96€ and 48x3=144€.

Data analysis techniques are introduced, including measures of central tendency and spread.

Definition: Mean (moyenne) is calculated as the sum of all values divided by the number of values.

Vocabulary: Median (médiane), quartiles, range (étendue).

The page also covers the calculation of median and quartiles, which are important for understanding data distribution.

Highlight: Quartiles divide ordered data into four equal parts, with Q1 at 25% and Q3 at 75% of the data.

Weighted average is briefly mentioned, showing how to account for different weights of data points.

Example: Weighted average = (ax1 + bx2 + cx2 + dx3) / (1 + 2 + 2 + 3)

These concepts are crucial for exercices corrigés in data analysis for 3ème students.

Voir

Page 3: Trigonometry and Equations

The final page covers trigonometry and equation solving, advanced topics in the Programme officiel maths 3ème PDF.

Basic trigonometric ratios (sine, cosine, tangent) are introduced in the context of right-angled triangles.

Example: In a right-angled triangle with an angle of 70°, cos(70°) = adjacent/hypotenuse.

Inverse trigonometric functions (arcsin, arccos, arctan) are also mentioned, showing how to find angles given trigonometric ratios.

Vocabulary: Fonctions trigonométriques réciproques (inverse trigonometric functions), arcsin, arccos, arctan.

The page concludes with a section on solving equations, emphasizing the importance of isolating the variable.

Highlight: When solving equations, remember to perform the same operations on both sides to maintain equality.

Example: Solving 3x + 5 = -4 = 3x + 2 + 3x involves combining like terms and isolating x.

These concepts are crucial for exercices Thalès et Pythagore corrigé 3ème and provide a foundation for more advanced mathematical studies.

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Knowunity est la meilleure application scolaire dans cinq pays européens.

Knowunity a été mis en avant par Apple et a toujours été en tête des classements de l'App Store dans la catégorie Éducation en Allemagne, en Italie, en Pologne, en Suisse et au Royaume-Uni. Rejoins Knowunity aujourd'hui et aide des millions d'étudiants à travers le monde.

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Knowunity est la meilleure application scolaire dans cinq pays européens.

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Les élèsves utilisent Knowunity

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Louis B., utilisateur iOS

J'aime tellement cette application [...] Je recommande Knowunity à tout le monde ! !! Je suis passé de 11 à 16 grâce à elle :D

Stefan S., utilisateur iOS

L'application est très simple à utiliser et bien faite. Jusqu'à présent, j'ai trouvé tout ce que je cherchais :D

Lola, utilisatrice iOS

J'adore cette application ❤️ Je l'utilise presque tout le temps pour réviser.

Matières

Maths

Géométrie

Dans les triangles

Théorème de thalès

Programme Maths 3ème 2024: Exercices Corrigés & Théorème de Thalès

Julien

@revaliiuwu

22 Abonnés

Suivre

The overall summary and page-by-page summaries for the provided PDF transcript are as follows:

19/04/2022

10357

Maths

346

Page 1: Geometric Theorems

This page focuses on fundamental geometric theorems crucial for maths 3ème students. It covers the Pythagoras' theorem, its converse, and Thales' theorem.

The Pythagoras' theorem is presented for right-angled triangles, stating that the square of the hypotenuse equals the sum of squares of the other two sides.

Definition: In a right-angled triangle, BC² = AC² + AB², where BC is the hypotenuse.

The converse of Pythagoras' theorem is also explained, which is used to determine if a triangle is right-angled.

Example: For triangle NYC, if NC² = NY² + YC² (3² + 4² = 5²), then NYC is a right-angled triangle.

Thales' theorem is introduced for similar triangles, showing the proportionality of corresponding sides.

Highlight: Thales' theorem states that AM/AB = MN/BC = AN/AC for similar triangles AMN and ABC.

The page concludes with a note on using cross multiplication to find missing values in Thales' theorem applications.

Vocabulary: Théorème de Thalès (Thales' theorem), Théorème de Pythagore (Pythagoras' theorem), hypotenuse, right-angled triangle.

Page 2: Ratios and Data Analysis

This page delves into ratios and data analysis techniques, essential components of the Programme maths 3ème.

The concept of ratios is explained, showing how to express relationships between numbers and divide quantities proportionally.

Example: To share 240€ between two people in the ratio 2:3, divide 240 by (2+3)=5, then multiply by respective ratio parts: 48x2=96€ and 48x3=144€.

Data analysis techniques are introduced, including measures of central tendency and spread.

Definition: Mean (moyenne) is calculated as the sum of all values divided by the number of values.

Vocabulary: Median (médiane), quartiles, range (étendue).

The page also covers the calculation of median and quartiles, which are important for understanding data distribution.

Highlight: Quartiles divide ordered data into four equal parts, with Q1 at 25% and Q3 at 75% of the data.

Weighted average is briefly mentioned, showing how to account for different weights of data points.

Example: Weighted average = (ax1 + bx2 + cx2 + dx3) / (1 + 2 + 2 + 3)

These concepts are crucial for exercices corrigés in data analysis for 3ème students.

Page 3: Trigonometry and Equations

The final page covers trigonometry and equation solving, advanced topics in the Programme officiel maths 3ème PDF.

Basic trigonometric ratios (sine, cosine, tangent) are introduced in the context of right-angled triangles.

Example: In a right-angled triangle with an angle of 70°, cos(70°) = adjacent/hypotenuse.

Inverse trigonometric functions (arcsin, arccos, arctan) are also mentioned, showing how to find angles given trigonometric ratios.

Vocabulary: Fonctions trigonométriques réciproques (inverse trigonometric functions), arcsin, arccos, arctan.

The page concludes with a section on solving equations, emphasizing the importance of isolating the variable.

Highlight: When solving equations, remember to perform the same operations on both sides to maintain equality.

Example: Solving 3x + 5 = -4 = 3x + 2 + 3x involves combining like terms and isolating x.

These concepts are crucial for exercices Thalès et Pythagore corrigé 3ème and provide a foundation for more advanced mathematical studies.

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Fiche mathématicien : René Descartes

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223

Maths - Fiche de révision sur Thalès

Fiche de révision sur le théorème de Thalès et sa réciproque.

2875

Maths - Fiche revision maths

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Maths - Théorème de Thalès

fiche de révision sur le théorème de Thalès.

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Rien ne te convient ? Explore d'autres matières.

Knowunity est la meilleure application scolaire dans cinq pays européens.

Knowunity a été mis en avant par Apple et a toujours été en tête des classements de l'App Store dans la catégorie Éducation en Allemagne, en Italie, en Pologne, en Suisse et au Royaume-Uni. Rejoins Knowunity aujourd'hui et aide des millions d'étudiants à travers le monde.

Chargement dans le

Google Play

Chargement dans le

App Store

4.9+

Note moyenne de l'appli

13 M

Les élèsves utilisent Knowunity

#1

Dans les palmarès des applications scolaires de 12 pays

950 K+

Les élèves publient leurs fiches de cours

Tu n'es toujours pas convaincu ? Regarde ce que disent les autres élèves ...

Louis B., utilisateur iOS

J'aime tellement cette application [...] Je recommande Knowunity à tout le monde ! !! Je suis passé de 11 à 16 grâce à elle :D

Stefan S., utilisateur iOS

L'application est très simple à utiliser et bien faite. Jusqu'à présent, j'ai trouvé tout ce que je cherchais :D

Lola, utilisatrice iOS