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.

**Example**

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 = \[\left( 4+5 \right)\text{ }cm=9\text{ }cm.\]

**Example**

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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