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The Théorème de Thalès exercice corrigé PDF and fraction simplification exercises demonstrate key mathematical concepts through practical problem-solving.
Key points:
16/03/2022
115
This exercise focuses on the application of the Théorème de Thalès to calculate various lengths in a complex geometric figure. The problem provides a diagram with parallel lines and several given measurements.
Definition: The Théorème de Thalès states that a line parallel to one side of a triangle divides the other two sides in the same ratio.
The exercise begins by identifying that WQ is parallel to UP, which allows for the application of the Thales theorem. The goal is to find the exact values and approximate measurements (to the nearest millimeter) of RQ, SR, US, and MU.
Example: To find RQ, the Thales theorem is applied in triangle MQR: MP/MQ = SP/RQ, resulting in RQ = (10 x 5) / 7 ≈ 7.1 cm
The solution proceeds step-by-step, using the Thales theorem multiple times to calculate the required lengths:
Highlight: The exercise demonstrates how the Thales theorem can be applied repeatedly in a complex figure to find multiple unknown lengths.
This problem showcases the practical application of the Théorème de Thalès in solving geometric problems and highlights the importance of precise calculations in geometry.
This exercise combines the use of the Pythagorean theorem with given measurements to solve for unknown lengths in a right-angled triangle. The problem presents a diagram of triangle GTR, which is right-angled at T, with some known side lengths.
Definition: The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of squares of the other two sides.
The exercise is divided into two parts:
Highlight: The exact value of RT is given as 51 cm, which is a key piece of information for solving the rest of the problem.
To solve for RK, the exercise first calculates RG using the Pythagorean theorem in the right-angled triangle RTG:
RG² = RT² + TG² = 51² + 68² = 7225 RG = √7225 = 85 cm
Example: The Pythagorean theorem is then applied again in triangle RKG to find RK: RK² = RG² + GK² = 85² + 57² = 10479 RK ≈ 102.3 cm (to the nearest millimeter)
This exercise demonstrates the practical application of the Pythagorean theorem in solving complex geometric problems and highlights the importance of step-by-step problem-solving in mathematics.
Vocabulary: Décomposition en produit de facteurs premiers refers to the process of breaking down a number into its prime factors, which is a fundamental concept in number theory and algebra.
Continuation of the geometric problem using Théorème de Thalès Exercice corrigé 4ème principles.
Example: SR = MR - MS = (60/7) - 6 = 2.5 cm (rounded to nearest millimeter)
Highlight: Multiple applications of Thales' theorem to find different lengths in the same figure.
The final page covers a right triangle problem combining the Pythagorean theorem with previous concepts.
Definition: The Pythagorean theorem states that in a right triangle, a² + b² = c².
Example: RG² = RT² + TG² = 51² + 68² = 7225
Highlight: The solution requires multiple applications of the Pythagorean theorem to find RK = 102.3 cm.
This exercise demonstrates the process of prime factorization and its application in finding the greatest common divisor (GCD) of two numbers. It also shows how to simplify fractions and solve a practical problem involving the distribution of candies.
Definition: Prime factorization is the process of breaking down a number into the product of its prime factors.
The exercise begins by decomposing the numbers 6120 and 5712 into their prime factors:
6120 = 2 x 2 x 2 x 3 x 3 x 5 x 17 5712 = 2 x 2 x 2 x 2 x 3 x 7 x 17
Example: To find the common divisors, we identify the shared prime factors between the two numbers.
The exercise then lists all the common divisors of these two numbers, which include 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204, and 408.
Highlight: The greatest common divisor (GCD) of 6120 and 5712 is determined to be 408.
Finally, the exercise applies this knowledge to a practical scenario involving a confectioner distributing dragées and pebble-shaped candies. The solution shows that the confectioner can make 408 packets, each containing 14 pebble-shaped candies and 15 dragées.
Vocabulary: Fraction irréductible refers to a fraction that cannot be further simplified, which is achieved by dividing both the numerator and denominator by their greatest common divisor.
16
428
3e/5e
Théorème de Thales & Sa réciproque
Un petit résume de cours avec quelques exemples . n'oublie pas de liker et t'abonner
31
1159
3e/2nde
Théorème + reciproque de thales
detail du théorème de thales ainsi que de la réciproque
3
34
3e
Théorème de Thalès
Théorème et réciproque de thalès
82
2753
3e
Théorème de Thalès
Maths troisième
21
1079
3e
Fiche De Révidion Math Brevet
La meilleur fiche de revision pour avoir une tres bonne note a l'epreuve de mathematique au brevet ou brevet blanc
33
1611
3e
Théorème de Thales
❤️
Note moyenne de l'appli
Les élèsves utilisent Knowunity
Dans les palmarès des applications scolaires de 17 pays
Les élèves publient leurs fiches de cours
Louis B., utilisateur iOS
Stefan S., utilisateur iOS
Lola, utilisatrice iOS
The Théorème de Thalès exercice corrigé PDF and fraction simplification exercises demonstrate key mathematical concepts through practical problem-solving.
Key points:
Accès à tous les documents
Améliore tes notes
Rejoins des millions d'étudiants
En t'inscrivant, tu acceptes les Conditions d'utilisation et la Politique de confidentialité.
This exercise focuses on the application of the Théorème de Thalès to calculate various lengths in a complex geometric figure. The problem provides a diagram with parallel lines and several given measurements.
Definition: The Théorème de Thalès states that a line parallel to one side of a triangle divides the other two sides in the same ratio.
The exercise begins by identifying that WQ is parallel to UP, which allows for the application of the Thales theorem. The goal is to find the exact values and approximate measurements (to the nearest millimeter) of RQ, SR, US, and MU.
Example: To find RQ, the Thales theorem is applied in triangle MQR: MP/MQ = SP/RQ, resulting in RQ = (10 x 5) / 7 ≈ 7.1 cm
The solution proceeds step-by-step, using the Thales theorem multiple times to calculate the required lengths:
Highlight: The exercise demonstrates how the Thales theorem can be applied repeatedly in a complex figure to find multiple unknown lengths.
This problem showcases the practical application of the Théorème de Thalès in solving geometric problems and highlights the importance of precise calculations in geometry.
Accès à tous les documents
Améliore tes notes
Rejoins des millions d'étudiants
En t'inscrivant, tu acceptes les Conditions d'utilisation et la Politique de confidentialité.
This exercise combines the use of the Pythagorean theorem with given measurements to solve for unknown lengths in a right-angled triangle. The problem presents a diagram of triangle GTR, which is right-angled at T, with some known side lengths.
Definition: The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of squares of the other two sides.
The exercise is divided into two parts:
Highlight: The exact value of RT is given as 51 cm, which is a key piece of information for solving the rest of the problem.
To solve for RK, the exercise first calculates RG using the Pythagorean theorem in the right-angled triangle RTG:
RG² = RT² + TG² = 51² + 68² = 7225 RG = √7225 = 85 cm
Example: The Pythagorean theorem is then applied again in triangle RKG to find RK: RK² = RG² + GK² = 85² + 57² = 10479 RK ≈ 102.3 cm (to the nearest millimeter)
This exercise demonstrates the practical application of the Pythagorean theorem in solving complex geometric problems and highlights the importance of step-by-step problem-solving in mathematics.
Vocabulary: Décomposition en produit de facteurs premiers refers to the process of breaking down a number into its prime factors, which is a fundamental concept in number theory and algebra.
Accès à tous les documents
Améliore tes notes
Rejoins des millions d'étudiants
En t'inscrivant, tu acceptes les Conditions d'utilisation et la Politique de confidentialité.
Continuation of the geometric problem using Théorème de Thalès Exercice corrigé 4ème principles.
Example: SR = MR - MS = (60/7) - 6 = 2.5 cm (rounded to nearest millimeter)
Highlight: Multiple applications of Thales' theorem to find different lengths in the same figure.
Accès à tous les documents
Améliore tes notes
Rejoins des millions d'étudiants
En t'inscrivant, tu acceptes les Conditions d'utilisation et la Politique de confidentialité.
The final page covers a right triangle problem combining the Pythagorean theorem with previous concepts.
Definition: The Pythagorean theorem states that in a right triangle, a² + b² = c².
Example: RG² = RT² + TG² = 51² + 68² = 7225
Highlight: The solution requires multiple applications of the Pythagorean theorem to find RK = 102.3 cm.
Accès à tous les documents
Améliore tes notes
Rejoins des millions d'étudiants
En t'inscrivant, tu acceptes les Conditions d'utilisation et la Politique de confidentialité.
This exercise demonstrates the process of prime factorization and its application in finding the greatest common divisor (GCD) of two numbers. It also shows how to simplify fractions and solve a practical problem involving the distribution of candies.
Definition: Prime factorization is the process of breaking down a number into the product of its prime factors.
The exercise begins by decomposing the numbers 6120 and 5712 into their prime factors:
6120 = 2 x 2 x 2 x 3 x 3 x 5 x 17 5712 = 2 x 2 x 2 x 2 x 3 x 7 x 17
Example: To find the common divisors, we identify the shared prime factors between the two numbers.
The exercise then lists all the common divisors of these two numbers, which include 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204, and 408.
Highlight: The greatest common divisor (GCD) of 6120 and 5712 is determined to be 408.
Finally, the exercise applies this knowledge to a practical scenario involving a confectioner distributing dragées and pebble-shaped candies. The solution shows that the confectioner can make 408 packets, each containing 14 pebble-shaped candies and 15 dragées.
Vocabulary: Fraction irréductible refers to a fraction that cannot be further simplified, which is achieved by dividing both the numerator and denominator by their greatest common divisor.
Maths - Théorème de Thales & Sa réciproque
Un petit résume de cours avec quelques exemples . n'oublie pas de liker et t'abonner
16
428
0
Maths - Théorème + reciproque de thales
detail du théorème de thales ainsi que de la réciproque
31
1159
0
Maths - Théorème de Thalès
Théorème et réciproque de thalès
3
34
0
Maths - Théorème de Thalès
Maths troisième
82
2753
4
Maths - Fiche De Révidion Math Brevet
La meilleur fiche de revision pour avoir une tres bonne note a l'epreuve de mathematique au brevet ou brevet blanc
21
1079
0
Maths - Théorème de Thales
❤️
33
1611
2
Note moyenne de l'appli
Les élèsves utilisent Knowunity
Dans les palmarès des applications scolaires de 17 pays
Les élèves publient leurs fiches de cours
Louis B., utilisateur iOS
Stefan S., utilisateur iOS
Lola, utilisatrice iOS
