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Shapes and Angles

Shapes and Angles

Look around yourself. What do you see? Buildings, trees, books, tables, chairs, notebooks, sun, moon, stars, etc. Are they all same? Do they have the same shape? No, not all of them are alike. The shape of the sun is different from that of a book. The notebooks are of the same shape but different size. Today we will discuss the various shapes and the properties of these shapes.

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Shapes

What is shape? The literal meaning of shape is the external form of a thing or its appearance. A figure can be made of different types of shapes. Figures can be broadly classified as open or closed. Open figures are those which do not end where they start. The figures that start and end at the same point are closed figures.

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Classification of Shapes

Let us learn more about the closed figure.  The shapes are made of lines or line segments arranged in an organized manner. Every object around us has a definite shape. Shapes can be classified into curves (circles) and polygons.

Polygons

A polygon is a simple closed figure with three or more than three line segments. Poly means “many”.

Terminologies Associated with Polygon

  • Sides: The lines segments that form the exterior of the polygon are the sides of the polygons.
  • Adjacent Sides: Two sides of a polygon having a common end-point are adjacent to each other.
  • Vertex: The point where the sides of a polygon meet is called the vertex of the polygon. It is also referred to as end-point. The plural of vertex is vertices.
  • Adjacent Vertices: The end-points of the same side of a polygon are adjacent vertices.

Polygons are classified into Regular and Irregular Polygons. A Polygon in which all sides and all angles are equal is a regular polygon. The sum of all interior angles of a regular polygon = 180° × (n − 2), where n is the number of sides. A Polygon in which all sides and all angles are not equal is an irregular polygon.

Types of Polygons

Let us discuss the types of polygons on the basis of the number of sides.

Triangles

A polygon bounded by three line segments or sides is a triangle. The sum of the interior angle of a triangle is 180°. On the basis of equality of sides, triangles are of three types:

  • Equilateral Triangle: A triangle with all sides equal is an equilateral triangle.

Shapes

  • Isosceles Triangle: A triangle with two sides of equal length is an isosceles triangle.

Shapes

  • Scalene Triangle: A scalene triangle is the one with all unequal sides.

Shapes

On the basis of the measure of angles, triangles are of following types:

  • Acute-angled Triangle: A triangle in which each angle is acute (less than 90°) is an acute-angled triangle.

Shapes

  • Right-angled Triangle: A right-angled triangle is the one in which one of the angles is a right angle (90°).

Shapes

  • Obtuse-angled Triangle: An obtuse-angled triangle is the one in which one of the angles is obtuse.

Shapes

  • Equiangular Triangle: If all the three angles are equal, the triangle is an equiangular triangle.

Shapes

Quadrilaterals

A closed figure bounded by four line segments is known as a quadrilateral. A quadrilateral has four sides, four vertices, and four angles. There are various types of the quadrilateral.

Parallelogram

A quadrilateral in which the pairs of opposite sides are parallel is a parallelogram. The sides of a quadrilateral that have no common endpoint are opposite sides.

Shapes

Properties of a Parallelogram:

  • Opposite sides are equal and parallel.
  • Opposite angles are equal
  • Diagonals bisect each other.

Rectangle

A rectangle is a special case of a parallelogram. In a rectangle, each angle is of 90°.

Shapes

Properties of a Rectangle:

  • Opposite sides are equal and parallel.
  • All angles are right angles
  • Both the diagonals are equal in length and bisect each other.

Square

A parallelogram with all sides of the same length and all the angles of 90° is a square.

Shapes

Properties of a Square:

  • All sides are equal.
  • Opposite sides are parallel (||).
  • All angles are right angles.
  • Both the diagonals are equal in length and bisect each other at right angles.

Rhombus

A parallelogram in which all the four sides are equal in length is a rhombus. A square is a special type of rhombus.

Shapes

Properties of Rhombus:

  • All sides are equal in length.
  • Opposite sides are parallel.
  • Opposite angles are equal.
  • The diagonals bisect each other at right angles.

Trapezium

A quadrilateral in which only one pair of opposite sides is parallel is a trapezium.

Shapes

Kite

A quadrilateral in which two pairs of adjacent sides are equal is a kite. Its diagonals bisect each other at right angle.

Shapes

Pentagon

It is a five-sided polygon. The sum of the interior angles of a pentagon is 540°. ABCDE is a regular pentagon with all equal sides.

Shapes

Hexagon

A hexagon is a six-sided polygon. The sum of the angles is 720°.

Shapes

A polygon with seven sides is a heptagon. With 8 sides it is an octagon. A 9-sided polygon is a nonagon.

Circle

When a set of points is at the same distance from a fixed point the figure obtained is a circle.

Terminologies Associated with Circle

  • Centre: The fixed point of the circle which is equidistance from all the points on the circle is its centre. Point O is the centre of the circle.
  • Radius: The line segment with one endpoint at the centre and the other on the boundary of the circle is a radius of the circle. OA is the radius of the circle.
  • Diameter: A line segment with both of its endpoints on the boundary of the circle and passes through the centre is the diameter of the circle. AB is the diameter of the circle. Diameter  = 2 × Radius.

Shapes

  •  Chord: Any line segment with its endpoints on the boundary of the circle is a chord. The diameter is the longest chord which passes through the centre. AB is a chord of the circle.

Shapes

  •  Circumference:  The length of the circle is the circumference of the circle.
  •  Arc: A part between any two points on a circle is an arc.

Shapes

  • Semicircle: Half of a circle is semicircle. Each part is a semicircle. A diameter divides a circle into two semicircles.

Shapes

Solved Examples for You

Problem: If the diameter of a circle is 40 cm, what is the value of its radius?
Solution: Diameter  = 2 × Radius.
Solving we have, Radius = 40 / 2 = 20 cm.

Problem: What is the name of a polygon with the smallest number of sides?
Solution: Triangle (with 3 sides).

Problem: Is a triangle possible with angles 54°, 63°, and 92°?
Solution: No, the sum of the angles = 54° + 63° + 92° = 209° which is not possible. The sum of angles of the triangle must be 180°.

Question: What are the basic geometric shapes?

Answer: The basic geometric shapes are defined as the figure or area barred by a border that forms by joining the particular amount of the curves, points, and lines. Some basic geometric shapes are triangle, circle, square, rectangle, etc. we all are aware of the basic shapes in geometry but there are a lot of other shapes also.

Question: What is a 3 sided shape called?

Answer: A 3-sided shape is commonly known as a triangle. Triangles are basically the polygons with 3 sides. Therefore, any polygon that is having 3 sides is known as a triangle. Triangle is one of the most popular basic shapes in geometry.

Question: What shape is a warning sign?

Answer: A Warning Sign can be of different shape and size. Many road signs warn us to slow down our speed or to watch for hazards or special conditions ahead in the way. Mostly the warning signs are yellow in color and are diamond-shaped with black letters and symbols.

Question: What shape is a trapezoid?

Answer: A trapezoid is basically a shape that has 4 sides with a minimum of one set of parallel sides. It can have 2 parallel sides and can become a parallelogram as well. However, if 2 sides are not parallel, then it’s just a basic trapezoid.

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