4th Class Mental Ability Geometry Geometrical Shapes

 

Geometrical Shapes

 

 

 

OBJECTIVES

 

·      To identify different objects with represent some kind of geometrical shapes which we are coming across our day to day life. (Both 2D and 3D)

·      To recognize difference parts of various geometrical shapes such as vertex and sides of a particular geometrical pattern.

·      Use of different geometrical shapes for creating Tangrams.

·      Knowledge of line of symmetry. (Horizontal and vertical)    

 

 

 

GEOMETRIC SHAPES

 

Geometric Shape is defined as a set of points or vertices and sides connecting to the point to form a closed entry. There are various kinds of geometrical shapes. Basing upon the number of vertices and sides they are identified.

 

          2d Geometrical Shapes

 

	·     Triangle has three sides. ·     It has three vertices.
	·     Squares have 4 equal sides and 4 right angles. ·     They have 4 lines of symmetry. ·     All squares belong to the rectangle family. ·     All squares belong to the rhombus family. ·     All squares are also parallelograms.
	·     Rectangles have 4 sides and 4 right angles. ·     They all have 2 lines of symmetry (4 lines if they are also a square!) ·     All rectangles belong to the parallelogram family.
	·     Rhombuses (rhombii) have 4 equal sides. ·     Both pairs of opposite sides are parallel. ·     They all have 2 lines of symmetry (4 lines if they are a square) ·     All rhombuses belong to the parallelogram family.
	·     Parallelograms have 2 parts of parallel sides. ·     Some parallelograms have lines of symmetry (depending on whether they are also squares, rectangles or rhombuses), but most do not.
	·     Circles have a point in the center from which each point on the diameter is equidistant. ·     They have infinite lines of symmetry.
	·     Ellipse are like circles which have been squashed or stretched. ·     They have 2 lines of symmetry. ·     They are also a special type of oval. ·     They longest and shortest diameters of the ellipse are called the major and minor axes. These axes are also the lines of symmetry.
	·     Crescent shapes are made when two circles overlap, or when one circle is removed from another circle. ·     The perimeter of crescent made from two circular arcs. ·     They have one line of symmetry. ·     Our moon forms crescent shapes during its phases.
	·     5 sides polygon
	·     6 sides polyon
	·     7 sides polygon
	·     8 sides polygon

 

3D Geometrical Shapes

	·  Cubes have 6 faces, 12 edges and 8 vertices. ·  All sides on a cube are equal length. ·  All faces are square in shape. ·  A cube is a type of cuboid.
	·  Cuboids have 6 faces, 12 edges and 8 vertices. ·  All the faces on a cuboid are rectangular.
	·  Spheres have either 0 or 1 faces, 0 edges and 0 vertices.
	·     Cylinders have either 2 or 3 faces, 0 or 2 edges, and 0 vertices.
	·     Cones have either 1 or 2 faces, 0 or 1 edges, and 1 apex (which is described by some mathematicians as a vertex).

 

 

 

 

REGULAR GEOMETRIC SHAPE

 

 

The geometric shapes whose all sides are equal sides and equal interior angles are known as regular geometric shape.

 

 

 

IRREGULAR GEOMETRIC SHAPES

 

 

The geometric shapes which have sides and angles of any length and size.

 

 

Direction (Examples 1 and 2): Answer the questions based on given figure (X).

                

 

 

Example 1:

How many rectangles are three in the given figure (X)?

(a) 10                           (b) 9           

(c) 8                             (d) 7

(1-2) The figure may be labelled as shown.

              

 

Ans.   (b)

The simplest rectangles are ABJI, BCKJ, IJFG and JKEF i.e. 4 in number.

The rectangles composed of two components each are ACKI, BCEF, IKEG and

ABFG i.e. 4 in number.

The only rectangle composed of four components is ACEG.

Thus, there are 4+4+1=9 rectangles in the given figure.

 

 

 

Example 2:

How many triangles are there in the given figure (X).

(a) 1                             (b) 2            

(c) 3                             (d) 4

 

Ans.    (d)

Triangles are:

A AHG, ACKD, AKED and ACDE i.e. 4 in number.

 

 

 

Example 3:

In the four alternatives a, b, c and d given below there are four different geometric shapes. Which among these is an irregular geometric shape?

(a)                (b)

(c)                  (d)

 

Ans.    (c)

The figure C is an irregular geometry shape.

 

 

 

TANGRAMS

 

These are the dissection puzzles which have seven different pieces of three geometrical shapes placed in specific numbers. The pieces are arranged in such manner that it reflects various features of real life like houses, people, animals, fruits etc. They are made in such a way that they are easily identifiable.

Here three tangram images are given below. Identify each one of them.

The three images serially are

(A)  A person in a running posture

(B)  A fish

(C) A horse

 

 

Example 4:

Which of the three images given above is having square in place of its head?

(a) A                            (b) B           

(c) C                            (d) None of these

 

Ans.    (a)

The man in running posture in image A is having a square in place of its head.

 

 

SYMMETRY

 

When an object is cut from the middle gives two equal parts of the main item then it is known as symmetrical object. On the other hand when the sub divided parts are not at all equal to each other it is called as asymmetric object.

There are some symmetrical objects which are given below:

    

The line from which the image is cut into two equal parts is known as Line of symmetry which can be further divided into horizontal line of symmetry and vertical line of symmetry.                                          

 

 

 

HORIZONTAL LINE OF SYMMETRIY

 

When a line divides an object in such a way that both the upper and lower parts of the image will be equally opposite to each other, it is known as horizontal line of Symmetry.

                    

            Horizontal line of Symmetry

 

 

 

VERTICAL LINE OF SYMMETRY

 

When a line divides an object in such a way the image in the right hand side is equally opposite to the image of the left hand side, it is known as vertical line of Symmetry.

Vertical line of symmetry

 

 

Example 5:

How many letters given below have at least one line of symmetry?

            (a) 5                             (b) 6           

            (c) 7                             (d) None

 

Ans.    (a)

 

    

Dotted lines are lines of symmetry.