What is Geometry?
Geometry is a discipline of mathematics that explores how things are measured in terms of their sizes, forms, angles, and dimensions.
2D shapes are flat shapes such as squares, circles, and triangles that are part of flat geometry. These forms only have two dimensions: length and width.
Solid objects are also known as 3D objects having the third dimension of height or depth. Examples of 3D shapes in solid geometry- are cube, cuboid, cone, and sphere.
Geometry is a branch of mathematics concerned with the study of points, lines, forms, and surfaces. Shapes, area, and volume are usually the first things that come to mind when you hear the word “geometry,” and that is exactly what geometry is!
Geometry, like algebra, is founded on a set of mathematical rules. These laws are known as axioms in geometry, and there are five major ones that you should be aware of.
Geometry is a discipline of mathematics that studies the shape of individual objects, their spatial connections, and the qualities of surrounding space. It is one of the oldest fields of mathematics, having developed in response to practical issues such as those encountered in surveying. Its name is derived from Greek words that indicate “Earth measuring.” It was eventually understood that geometry did not have to be restricted to the study of flat surfaces (plane geometry) and rigid three-dimensional objects (solid geometry), but that it could be used to represent and develop even the most abstract thoughts and visions.
5 axioms of Geometry-
Axioms are employed as the building blocks of problem-solving in Euclidean Plane Geometry, which is the main sort of geometry taught in high school mathematics. Axioms, which are employed in high school geometry, are based on the work of the ancient Greek mathematician Euclid and allow us to derive certain mathematical truths from a few fundamental notions. Euclid is recognized as the “Father of Geometry,” and his book The Elements is the first textbook on the topic.
These 5 axioms of geometry are:
- A straight line can be drawn between any two points. A straight line can connect any two places in the same plane (or flat area). This axiom means that you can “connect the dots.”
- Straight-line can be extended indefinitely Straight lines can go to infinity and beyond.
- A circle can be made using any point in its centre and a line segment as its radius. According to this axiom, you may draw a circle around any point in a plane. The radius of the circle will extend from the dot to the circle’s edge, making a straight line.
- All right angles are congruent Every right angle is the same. There are no more or less than 90 degrees at any right angle.
- PARALLEL POSTULATE: GIVEN A STRAIGHT LINE AND A POINT (NOT ON THE LINE), THERE IS ALWAYS A SECOND STRAIGHT LINE THROUGH THE POINT THAT WILL BE PARALLEL TO THE FIRSTLINE.
Essentially, this postulate states that if two lines are on the same plane, we can always draw a second line parallel to them.
Geometry Formulas
Geometry Shapes Formulas for Class 10 | |
Name | Formula |
Area of Triangle | Area= ½ × base × height |
Pythagorean Theorem | a^{2 }+ b^{2 }= c^{2} |
Area of a Circle | Area = πr^{2} |
Circumference of a Circle | C = 2πr or πd |
Area of a Parallelogram | Area = base × height |
Area of a Trapezoid | Area = ½ × (base_{1} + base_{2}) × height |
Area of a Kite or a Rhombus | Area = ½ × (diagonal_{1 }× diagonal_{2}) |
Area of a Square | Area = side^{2} |
Area of a Regular Polygon | Area = ½ × perimeter × apothem |
Number of Diagonal in n-sided Polygon | Diagonals = ½ × n(n−3) |
Slope | m = (y_{2}−y_{1})/(x_{2}−x_{1}) = rise/run |
Midpoint Formula | (x_{mp}, y_{mp}) = [(x_{1}+x_{2})/2],[(y_{1}+y_{2})/2] |
Distance Formula | d = √[(x_{2}−x_{1})^{2}+(y_{2}−y_{1})^{2}] |
Equation of a Circle | (x−h)^{2}+(y−k)^{2} = r^{2} |
FAQs on Class 10 Geometry Formulas
A. How to memorize geometry formulas?
The first and most important step in learning Geometry is to cease thinking of it as a difficult subject. Don’t just cram and try to figure out what that formula is supposed to solve. You won’t forget what real-life problem a Geometry formula solves for the rest of your life once you discover it.
B. How to be good in geometry formulas?
The best way to excel at Class 10 Geometry formulae is to understand the concepts behind the formulas rather than memorize them. You will never forget the formulas if you do it this way.
C. How is Geometry used?
Almost everyone uses geometry on a daily basis, even if they have never opened a geometry book. When you get out of bed in the morning or parallel park a car, your brain does geometric spatial computations. Geometry is the study of spatial perception and geometric reasoning.
Geometry can be found in a variety of mediums, including art, architecture, engineering, robotics, astronomy, sculptures, space, nature, sports, machinery, and automobiles. A compass, protractor, square, graphing calculators, Geometer’s Sketchpad, and rulers are all common geometry equipment. Geometry includes several core abilities and aids in the development of logic, deductive reasoning, analytical reasoning, and problem-solving thinking skills.
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Geometry in early schooling
Geometry classes in school help students improve spatial reasoning and problem-solving skills. Geometry is intertwined with a variety of other math concepts, particularly measurement.
The geometric focus in early learning tends to be on forms and solids. After that, you’ll study the properties and relationships of shapes and solids. Problem-solving skills, logical reasoning, transformations, symmetry, and spatial thinking will all be introduced.
Geometry in Later Schooling
Geometry becomes increasingly about analysis and reasoning as abstract thinking grows. Analyzing properties of two- and three-dimensional shapes, reasoning about geometric relationships, and using the Co-ordinate geometry are all topics that are covered throughout high school. Geometry instruction provides several fundamental skills and aids in the development of logic, deductive reasoning, analytical reasoning, and problem-solving abilities.