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In a figure AC=XD ,C is the mid point of AB, D is the mid point of XY. Using Euclid axiom show AB = XY?
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In a figure AC=XD ,C is the mid point of AB, D is the mid point of XY....
**Euclid's Axioms:**
Euclid's axioms are a set of postulates that form the foundation of Euclidean geometry. These axioms are assumptions that are considered to be self-evident truths. One of the axioms states that a line segment can be divided into two equal parts by its midpoint.
**Given Information:**
In the given figure, AC is equal to XD. Additionally, point C is the midpoint of line segment AB, and point D is the midpoint of line segment XY.
**Proof:**
To prove that AB is equal to XY using Euclid's axioms, we can follow these steps:
1. Draw a figure representing the given information, with line segments AC, XD, AB, and XY.
2. Label the points as shown in the figure.
3. Since C is the midpoint of AB, we can apply Euclid's axiom that states a line segment can be divided into two equal parts by its midpoint. This means that AC is equal to CB.
4. Similarly, since D is the midpoint of XY, we can apply the same axiom to conclude that XD is equal to DY.
5. Since AC is equal to CB and XD is equal to DY, we can substitute these values into the equation AC = XD.
6. This gives us AC + CB = XD + DY.
7. By rearranging the terms, we have AB + AB = XY + XY.
8. Simplifying the equation, we get 2AB = 2XY.
9. Dividing both sides of the equation by 2, we obtain AB = XY.
10. Therefore, we have proven that AB is equal to XY using Euclid's axiom.
In conclusion, by applying Euclid's axiom that states a line segment can be divided into two equal parts by its midpoint, we can show that AB is equal to XY in the given figure.
Euclid's axioms are a set of postulates that form the foundation of Euclidean geometry. These axioms are assumptions that are considered to be self-evident truths. One of the axioms states that a line segment can be divided into two equal parts by its midpoint.
**Given Information:**
In the given figure, AC is equal to XD. Additionally, point C is the midpoint of line segment AB, and point D is the midpoint of line segment XY.
**Proof:**
To prove that AB is equal to XY using Euclid's axioms, we can follow these steps:
1. Draw a figure representing the given information, with line segments AC, XD, AB, and XY.
2. Label the points as shown in the figure.
3. Since C is the midpoint of AB, we can apply Euclid's axiom that states a line segment can be divided into two equal parts by its midpoint. This means that AC is equal to CB.
4. Similarly, since D is the midpoint of XY, we can apply the same axiom to conclude that XD is equal to DY.
5. Since AC is equal to CB and XD is equal to DY, we can substitute these values into the equation AC = XD.
6. This gives us AC + CB = XD + DY.
7. By rearranging the terms, we have AB + AB = XY + XY.
8. Simplifying the equation, we get 2AB = 2XY.
9. Dividing both sides of the equation by 2, we obtain AB = XY.
10. Therefore, we have proven that AB is equal to XY using Euclid's axiom.
In conclusion, by applying Euclid's axiom that states a line segment can be divided into two equal parts by its midpoint, we can show that AB is equal to XY in the given figure.
Community Answer
In a figure AC=XD ,C is the mid point of AB, D is the mid point of XY....
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In a figure AC=XD ,C is the mid point of AB, D is the mid point of XY. Using Euclid axiom show AB = XY?
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In a figure AC=XD ,C is the mid point of AB, D is the mid point of XY. Using Euclid axiom show AB = XY? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about In a figure AC=XD ,C is the mid point of AB, D is the mid point of XY. Using Euclid axiom show AB = XY? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a figure AC=XD ,C is the mid point of AB, D is the mid point of XY. Using Euclid axiom show AB = XY?.
In a figure AC=XD ,C is the mid point of AB, D is the mid point of XY. Using Euclid axiom show AB = XY? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about In a figure AC=XD ,C is the mid point of AB, D is the mid point of XY. Using Euclid axiom show AB = XY? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a figure AC=XD ,C is the mid point of AB, D is the mid point of XY. Using Euclid axiom show AB = XY?.
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