Geometrical Shapes
Category : 3rd Class
Geometrical Shapes
Introduction
Lines, angles and rays are the basic concept of geometrical figures. Basic geometrical figure was first introduced in text by great mathematician Euclid.
Lines and Its Characteristics
Point
A precise location or place on a plane. Point is usually represented by dot.
\[\bullet \xrightarrow{{}}A\]
A is a point
Line
Line is a geometrical figure formed by points moving along a fixed direction and the reverse direction. Line may be straight or curved.
Line Segment
A straight line which links two points without extending beyond them.
Ray
A ray extends infinity in one direction, but ends at a single point in the other direction.
Intersecting Point
The point where two lines meet or cross.
In the pictures above points J, K, L, M and 0 are intersecting points.
To Draw a Line Segment of a given Length.
The following are the steps used to draw the line segment
For example: Line segment of 6 cm.
Step 1: place the ruler on the plane paper.
Step 2: Mark a point A on the paper against 0 mark of ruler
Step 3: Mark another point B on the same paper at the length of 6 cm.
Step 4: Draw a line between A and B.
AB is the required length of 6 cm.
AO = 4 cm and OB = 5 cm. Find the length of AB
(a) 9 cm (b) 5 cm
(c) 8 cm (d) 7 cm
(e) None of these
Answer (a)
Explanation: Length of AB = \[\left( 4+5 \right)\text{ }cm=9\text{ }cm.\]
Identify the line from the figures given below:
(a) 
(b) 
(c) 
(d) All the above
(e) None of these
Answer (c)
Explanation: A line is extended from both the ends.
Angles
When two or more lines meet at a point then angle is formed. A complementary of an angle is obtained by subtracting the angle from a right angle. A supplementary angle is obtained by subtracting the angle from a straight angle.
A Right Angle
An angle whose measure is exactly \[90{}^\circ \]is a right angle.
An Acute Angle
An angle whose measure is less than \[90{}^\circ \]is an acute angle.
An Obtuse Angle
An angle whose measure is greater than \[90{}^\circ \] but less than \[180{}^\circ \]is obtuse angle.
Straight Angle
An angle whose measure is \[180{}^\circ \]is a straight angle.
A Reflex Angle
An angle whose measure is greater than \[180{}^\circ \]but less than \[360{}^\circ \]is a reflex angle.
Triangles
A region bounded by three line segments is called triangular region and figure is triangle.
Equilateral Triangle
A triangle whose all sides are equal is called equilateral triangle.
Triangle ABC is an equilateral triangle.
Isosceles Triangle
A triangle whose two sides are equal is called isosceles triangle.
In triangle ABC AB = AC = 4 cm hence, triangle ABC is an isosceles triangle.
Scalene Triangle
A triangle whose sides are unequal is called scalene triangle. In the figure below Side length of tangle ABC are not equal hence, triangle ABC is a scalene triangle.
A Right Angle Triangle
A triangle whose one angle is a right angle is called right angled triangle. In the picture below triangle ABC is a right angle.
Rectangle and Square
Rectangle
A rectangle is a special type of quadrilateral in which:
(a) Opposite sides are equal.
(b) Both diagonals are equal, and
(c) Each angle is a right angle\[(90{}^\circ )\].
In the rectangle ABCD given above, AB = CD and AD = BC. Diagonals AC = BD and each angle is of\[90{}^\circ \].
Square
A Square is, special type of quadrilateral in which:
(a) All four sides are equal
(b) Both diagonals are equal, and
(c) Each angle is a right angle\[(90{}^\circ )\].
In the square ABCD given above, AB = BC = CD = AD and diagonal, AC = BD. Each angle is of\[90{}^\circ \]. A square is a special type of rectangle, but every rectangle is a square.
Circle
A circle is a simple closed shape with curved boundary each of whose point is at the same distance from a fixed point inside from affixed point inside it. A circle has no side or corners, like the square, rectangle and triangle.
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