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Prove that an equilateral triangle can be constructed on any given line segment
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Prove that an equilateral triangle can be constructed on any given lin...
Construction of an Equilateral Triangle on a Given Line Segment
Introduction
To construct an equilateral triangle on a given line segment means to draw an equilateral triangle with the given line segment as one of its sides. In this guide, we will explain how to construct an equilateral triangle on any given line segment.
Tools Required
To construct an equilateral triangle on a given line segment, we need the following tools:
- Ruler
- Compass
Steps to Construct an Equilateral Triangle on a Given Line Segment
To construct an equilateral triangle on a given line segment, follow these steps:
- Draw the given line segment using a ruler.
- Place the compass on one end of the line segment and draw an arc that intersects the line segment.
- Without changing the compass width, place the compass on the other end of the line segment and draw an arc that intersects the line segment at a point different from the first arc.
- Draw a straight line connecting the two points where the arcs intersect the line segment. This line will be the base of the equilateral triangle.
- Place the compass on one of the points where the arc intersects the line and draw an arc that passes through the other point where the arc intersects the line segment.
- Without changing the compass width, place the compass on the other point where the arc intersects the line segment and draw an arc that intersects the previous arc.
- Draw a straight line connecting the two points where the arcs intersect. This line will be the third side of the equilateral triangle.
Conclusion
By following these steps, we can construct an equilateral triangle on any given line segment. The resulting equilateral triangle will have the given line segment as one of its sides and will have all three sides of equal length.
Community Answer
Prove that an equilateral triangle can be constructed on any given lin...
In order to prove the above statement, follow the given steps:-
Step-1- Draw a line segment AB of any length.
Step-2- Taking A as a centre and radius = length of AB, draw an arc above the line segment AB.
Step-3- Now, taking B as a centre and the same radius, draw an arc intersecting the previous arc at the point C.
Step-4- Join AC and CB.
Step-5- ABC is the required equilateral triangle.
This construction proves that an equilateral triangle can be constructed on any line segment.
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Prove that an equilateral triangle can be constructed on any given line segment
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Prove that an equilateral triangle can be constructed on any given line segment 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 Prove that an equilateral triangle can be constructed on any given line segment covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Prove that an equilateral triangle can be constructed on any given line segment.
Prove that an equilateral triangle can be constructed on any given line segment 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 Prove that an equilateral triangle can be constructed on any given line segment covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Prove that an equilateral triangle can be constructed on any given line segment.
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