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The area may be defined as the quantity that is used to expresses the extent of a two-dimensional region, shape, in the plane. In the case of two dimensions and three dimensions, the area is analogous to the surface area.
Angle is formed at a point of intersection of two lines or rays. The angle may be formed by the intersection of two planes too. The angle is the measure of the turn between two lines or two planes.
A point in geometry is a method to show a location. Point is a dimensionless quantity as it has no size, no width, no length, and no depth. A point is represented by a dot. A line is defined as a line of points that extends infinitely in two directions and points that lie on the same line are called collinear points.
In mathematics, a plane is defined as a flat and two-dimensional surface that extends infinitely. A plane is the two-dimensional analog of a point (0 dimensions), a line (1D), and 3D space.
In mathematics/geometry, a line may be defined as a straight 1D figure that has no thickness and extends endlessly in both directions and is often described as the shortest distance between any two points.
A circle looks like a round-shaped figure that has no corners and has no edges. In mathematics/geometry, a circle may be defined as a closed, two-dimensional curved shape in which all the points on the cure are at a fixed distance from a point. This point is known as the center of a circle. This fixed distance from the center to the point on the curve is known as the radius of the circle.
In mathematics/geometry, a polygon is a plane figure that has a finite number of straight-line segments having a closed shape. The polygons do not have any curved sides i.e. all the lines are straight. Triangle is an example of the three-sided polygon. Similarly, four, five, six-sided polygon are called quadrilateral, pentagon, hexagon respectively.
Triangle may be defined as a three-sided polygon, i.e. It has three sides and three angles are formed at the intersection of three sides.
In mathematics, transformation may be defined as the process of converting a single form from one domain to another. The signal can be transformed from the time domain to the frequency domain or vice versa by using various transformation methods like Laplace Transformation, Fourier Transformation, etc.
Quadrilaterals may be defined as polygons having four sides. It has four angles. Square, rectangle, rhombus are examples of the quadrilateral.
In geometry, the similarity is the property when two figures are identical to each other.
Coordinate geometry is also known as analytic geometry may be defined as the study of geometry by making use of coordinate points. By using the coordinate geometry, we can find the distance between two points, dividing lines in the x:y ratio, finding the mid-point of a line, calculating the area of a triangle in the Cartesian plane, etc.
A triangle may be termed as a right-angled triangle if one angle of the triangle is 90 degrees. The side opposite to the right angle in the right triangle is called hypotenuse and the remaining two sides are known as base and perpendicular.
Trigonometry may be defined as a branch of mathematics that studies relationships between side lengths and angles of triangles by making use different trigonometric relationships on the triangle.
Two lines are said to be perpendicular if the angle between them is 90 degrees at the point of intersection whereas if two lines don't intersect with each other at any point even after infinite expansion at both ends, then the line is said to be a parallel line.
Q1. What is the exterior angle of the regular octagon?
Sol. Regular octagon have all angles equals
And by exterior angle sum property of polygons,
We have sum of all the exterior angle equals to 360°
So, 8×exterior angle=360°
exterior angle= 360°8
exterior angle= 45°
Q2. Find the arc length of a circle with radius 14 cm making an angle of 36° at the centre.
Sol. Radius of the = 14 cm
Angle at the centre = 36°
Arc length = e/360.2πr
= 36/360× 2× 22/7×14
= 8.8 cm
Q3. Find if the following triangles are congruent or not, If the two sides are equal.
Lets imagine one triangle as ABC and other as PQR
Sol. We have
AB = PQ ( from figure )
BC = QR ( from figure )
∠B = ∠Q ( from figure )
So, by side angle side congruency rule we have
Geometry is the oldest branch of Mathematics. For high school graduates taking at least three years of math, including algebra and geometry, is a minimum requirement. The typical course order is::
Geometry is usually taken in a student’s 2nd year of high school. The high school geometry curriculum introduces students to the concepts of basic trigonometry, angles of elevation and depression, and methods of proving triangle congruence.
If you are looking to be admitted to a good university or college after high school, then focusing on Geometry is very important. The University of California among other requirements asks students to study two- and three-dimensional geometry in order to get admission at the prestigious university.
Students can find many practical uses of geometry in daily life. Some examples of real-life applications of geometry are:
Students interested in Geometry can build successful careers in architecture, engineering, and contractors. Astronomy is another field that relies on geometry and can become a high-paying and rewarding career option for students.
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The best way to learn any branch of Math is practice. On the other hand getting help in geometry on time to avoid confusion later is also important. Apart from this you must:
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Point, line and plane are regarded as the basic concepts of geometry. To learn the fundamentals in the subject, you must also know:
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Geometry helps us in everyday life as right from the video games you play to the food design or shape of pizza, is all based on it.
To name a few fields, it is used in :
Whether it is robotics, fashion designing, geometry is used everywhere and a good knowledge in the subject opens numerous career options for a student.
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