Simple closed curves made up of only line segments are called polygons. Line segments that form the polygon are the sides of the polygon. Any two sides with a common end point are called the adjacent sides. The point of intersection of a pair of sides is called a vertex.
Geometry is the branch of mathematics that deals with the study of shapes, sizes, and properties of figures and spaces. It is a fundamental subject that provides a foundation for understanding and analyzing the physical world. Here are some basic geometrical ideas along with interesting facts:
1. Point: A point is a basic building block of geometry. It is a location in space and has no size or dimension. Points are represented by a dot and are named using capital letters. Interesting Fact: Despite having no dimensions, points are essential in defining all other geometric figures.
2. Line: A line is a straight path that extends indefinitely in both directions. It is made up of an infinite number of points. Lines are represented by a straight line segment with arrows at both ends. Interesting Fact: A line has no thickness and can be thought of as an infinitely thin object.
3. Ray: A ray is a part of a line that has one endpoint and extends infinitely in one direction. It can be thought of as a "half-line." Rays are represented by a line segment with a single arrowhead. Interesting Fact: A ray has no endpoint in the direction it extends, allowing it to continue indefinitely.
4. Line Segment: A line segment is a part of a line that has two distinct endpoints. It is a finite section of a line. Line segments are represented by a straight line with endpoints marked by small dots. Interesting Fact: The length of a line segment can be measured using a ruler or other measuring tools.
5. Angle: An angle is formed when two rays share a common endpoint, known as the vertex. Angles are measured in degrees (°) or radians. They can be acute (less than 90°), right (exactly 90°), obtuse (greater than 90° but less than 180°), or straight (exactly 180°). Interesting Fact: A full rotation around a point is equivalent to 360° or 2π radians.
6. Triangle: A triangle is a polygon with three sides and three angles. It is one of the most basic geometric shapes. Triangles can be classified based on their side lengths (equilateral, isosceles, or scalene) or their angle measures (acute, right, obtuse). Interesting Fact: The sum of the internal angles of a triangle is always 180°.
7. Quadrilateral: A quadrilateral is a polygon with four sides and four angles. Examples of quadrilaterals include squares, rectangles, parallelograms, and trapezoids. Interesting Fact: The sum of the internal angles of a quadrilateral is always 360°.
8. Circle: A circle is a two-dimensional shape that is perfectly round and consists of all points equidistant from a fixed center point. It has no straight sides or angles. Circles are represented by a curved line that encloses a circular region. Interesting Fact: The ratio of the circumference of a circle to its diameter is always constant and approximately equal to 3.14159, represented by the Greek letter π (pi).
These are just a few basic geometrical ideas that form the foundation of geometry. Exploring these concepts further can lead to a deeper understanding of shapes, spatial relationships, and the mathematical principles that govern our physical world.
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Answer:
Simple closed curves made up of only line segments are called polygons. Line segments that form the polygon are the sides of the polygon. Any two sides with a common end point are called the adjacent sides. The point of intersection of a pair of sides is called a vertex.
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Basic Geometrical Ideas:
Geometry is the branch of mathematics that deals with the study of shapes, sizes, and properties of figures and spaces. It is a fundamental subject that provides a foundation for understanding and analyzing the physical world. Here are some basic geometrical ideas along with interesting facts:
1. Point: A point is a basic building block of geometry. It is a location in space and has no size or dimension. Points are represented by a dot and are named using capital letters. Interesting Fact: Despite having no dimensions, points are essential in defining all other geometric figures.
2. Line: A line is a straight path that extends indefinitely in both directions. It is made up of an infinite number of points. Lines are represented by a straight line segment with arrows at both ends. Interesting Fact: A line has no thickness and can be thought of as an infinitely thin object.
3. Ray: A ray is a part of a line that has one endpoint and extends infinitely in one direction. It can be thought of as a "half-line." Rays are represented by a line segment with a single arrowhead. Interesting Fact: A ray has no endpoint in the direction it extends, allowing it to continue indefinitely.
4. Line Segment: A line segment is a part of a line that has two distinct endpoints. It is a finite section of a line. Line segments are represented by a straight line with endpoints marked by small dots. Interesting Fact: The length of a line segment can be measured using a ruler or other measuring tools.
5. Angle: An angle is formed when two rays share a common endpoint, known as the vertex. Angles are measured in degrees (°) or radians. They can be acute (less than 90°), right (exactly 90°), obtuse (greater than 90° but less than 180°), or straight (exactly 180°). Interesting Fact: A full rotation around a point is equivalent to 360° or 2π radians.
6. Triangle: A triangle is a polygon with three sides and three angles. It is one of the most basic geometric shapes. Triangles can be classified based on their side lengths (equilateral, isosceles, or scalene) or their angle measures (acute, right, obtuse). Interesting Fact: The sum of the internal angles of a triangle is always 180°.
7. Quadrilateral: A quadrilateral is a polygon with four sides and four angles. Examples of quadrilaterals include squares, rectangles, parallelograms, and trapezoids. Interesting Fact: The sum of the internal angles of a quadrilateral is always 360°.
8. Circle: A circle is a two-dimensional shape that is perfectly round and consists of all points equidistant from a fixed center point. It has no straight sides or angles. Circles are represented by a curved line that encloses a circular region. Interesting Fact: The ratio of the circumference of a circle to its diameter is always constant and approximately equal to 3.14159, represented by the Greek letter π (pi).
These are just a few basic geometrical ideas that form the foundation of geometry. Exploring these concepts further can lead to a deeper understanding of shapes, spatial relationships, and the mathematical principles that govern our physical world.
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