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Geometry
Introduction to Geometry

Geometry is a branch of mathematics that deals with the study of shapes, sizes, and positions
of objects in space
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The word "Geometry" is derived from the Greek word’s "geo" meaning
"earth" and "metron" meaning "measure
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These definitions provide a
foundation for the study of Geometry
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It is represented by a
dot
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It has no thickness and is
represented by a straight line with two arrows at the ends
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It is
represented by a straight line with one arrow at the end
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It is represented by a
straight line with two endpoints
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The common
endpoint is called the vertex of the angle
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Circle: A circle is a set of all points that are equidistant from a fixed point called the center of the
circle
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Some of the important formulas are:

Area of a Triangle: The area of a triangle is given by the formula A = (1/2)bh, where b is the base
of the triangle and h is its height
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Area of a Circle: The area of a circle is given by the formula A = πr^2, where r is the radius of the
circle
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Volume of a Sphere: The volume of a sphere is given by the formula V = (4/3)πr^3, where r is the
radius of the sphere
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Problem-Solving Techniques

To solve problems in Geometry, you need to apply the formulas and theorems that you have learned
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It can also help you to identify the given information and the unknowns
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Identify the given information and write it down
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Choose the Right Formula: Once you have identified the given information and the unknowns,
choose the formula that is appropriate for the problem
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Solve for the Unknown: Solve the equation to find the value of the unknown
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Types of Geometric Shapes

There are several types of geometric shapes that you will encounter in Geometry
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They are classified according to the length of their
sides and the measure of their angles
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There are also three types of triangles based on their angles:
acute, right, and obtuse
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They are classified based on their
properties, such as the length of their sides and the angles between them
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Circles: Circles are round shapes with a fixed radius and center point
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Polygons: Polygons are closed shapes with three or more sides
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Geometry Theorems

Geometry theorems are statements that have been proven to be true
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Some of the most important theorems are:

Pythagorean Theorem: The Pythagorean Theorem states that in a right triangle, the sum of the
squares of the lengths of the legs is equal to the square of the length of the hypotenuse
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Congruent Triangles Theorem: The Congruent Triangles Theorem states that if two triangles
have three corresponding sides that are congruent, then the triangles are congruent
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Applications of Geometry

Geometry has many applications in real life
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Art: Many artists use geometric shapes and patterns in their art, such as mosaics, tessellations,
and fractals
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Engineering: Geometry is used in engineering to design and analyze structures, machines, and
systems
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It involves a lot of formulas, theorems, and problem-solving techniques
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