Students can go through AP 6th Class Maths Notes Chapter 5 Understanding Elementary to understand and remember the concepts easily.
Class 6 Maths Chapter 5 Notes Understanding Elementary
→ A point determines a location. It is usually denoted by a capital letter.
‘P’ is a point on the line ‘l’. 
→ A line segment is formed by joining two points. It has a fixed length.
\(\overline{\mathrm{AB}}\) is a line segment. 
→ A line is obtained when a line segment extends on both sides indefinitely.
→ The line ‘n’ is obtained when \(\overline{\mathrm{PQ}}\) is extended on both sides indefinitely.
→ A ray is a portion of a line starting at a point and goes in one direction endlessly.
\(\overline{\mathrm{OA}}\) is a ray. It starts at ‘O’ and passes through the point A.
→ Any figure drawn without lifting a pencil may be called a curve. In this sense, a line is also a curve.
→ A simple curve is one that does not cross itself.
→ Curves are of two types – open find closed.
→ An angle is made up of two rays starting from a common end point. The common end point is called vertex and the two rays are arms of the angle.
‘O’ is the vertex. \(\overrightarrow{\mathrm{OA}}\) and \(\overrightarrow{\mathrm{OB}}\) are two arms or sides of the angle AOB or BOA.
Symbol : ∠AOB or ∠BOA; \(\hat{A O B}\) or \(\hat{B O A}\)
→ Every angle divides the plane as interior, exterior and boundary of the angle.
→ A triangle is a simple closed figure bounded by three line segments.
→ A triangle has three vertices, three sides and three angles.
A, B and C are the vertices of the triangle ABC.
AB, BC, CA are the sides of the triangle ABC.
∠BAC, ∠ABC, ∠ACB are the three angles of the triangle ABC.
→ A triangle with its boundary and interior is called the triangular region.
→ A quadrilateral is a simple closed figure bounded by four line segments. It has four vertices, four sides, four angles and two diagonals.
\(\overline{\mathrm{AB}}\), \(\overline{\mathrm{BC}}\), \(\overline{\mathrm{CD}}\), \(\overline{\mathrm{DA}}\) are the four sides of the quadrilateral ABCD.
A, B, C, D are its vertices.
∠DAB, ∠ABC, ∠BCD, ∠CDA are its angles.
\(\overline{\mathrm{AC}}\) and \(\overline{\mathrm{BD}}\) are its two diagonals.
→ A circle is a simple closed curve, where each point on the boundary is at an equal distance from the centre. The fixed distance is the radius.
→ A part of a circle is an arc and the total length of the circle is called its circumference.
→ A chord of a circle is a line segment joining any two points on the circle. Diameter is also a chord.
→ A diameter of a circle is double the radius.
→ A circle with its boundary and interior together is a circular region.
→ The region in a circle bounded by two radii and the arc is called sector.
→ The region in a circle bounded by a chord and the arc is called a segment, of the circle.
→ A semi-circle is half of the circle. Each diameter divides a circle into two semi-circles.
→ We compare two line segments by simple observation, by tracing the line segments and by using instruments.
→ The instruments used to compare and draw line segments are ruler and divider.
→ The unit of measuring length is 1 centimeter (1 cm); 1 cm = 10 mm.
→ A protractor is a semi circular curved model with 180° equal divisions used to measure and construct angles.
→ The unit of measuring an angle is a degree (1°). It is \(\frac{1}{360}\)th part of one revolution.
→ The measure of right angle is 90° and that of a straight angle is 180°.
→ An angle is acute if its measure is smaller than a right angle.
→ An angle is obtuse if its measure is more than that of a right angle and less than a straight angle.
→ A reflex angle is more than a straight angle.
→ Two distinct lines of a plane which have a common point are intersecting lines.
→ Two intersecting lines are peipendicular if the angle between them is a right angle.
→ If two lines of a plane do not intersect each other then they are called parallel lines.
→ Two parallel lines do not have any common point.
→ Angles where the ray moves in the opposite direction of the hands of a clock are called anticlockwise angles.
\(\overrightarrow{\mathrm{OA}}\) is the initial ray. It is moved in the opposite direction of the hands of a clock and reached
\(\overrightarrow{\mathrm{OB}}\), making an angle AOB.
→ Angles where the ray moves in the direction of the hands of a clock are called clock¬wise angles.
\(\overrightarrow{\mathrm{OA}}\) is the initial ray.
It is moved in the direction of the hands of a clock and reached \(\overrightarrow{\mathrm{OB}}\), making an angle AOB.
→ Kinds of Angles :
→ Lines :
→ The distance between the end points of a line segment is its length.
→ A graduated ruler and the divider are useful to compare lengths of line segments.
→ When a hand of a clock moves from one position to another position we have an ex¬ample for an angle.
One full turn of the hand is 1 revolution.
A right angle is lA revolution and a straight angle is 1/2 a revolution.
We use a protractor to measure the size of an angle in degrees.
The measure of a right angle is 90° and hence that of a straight angle is 180°.
An angle is acute if its measure is smaller than that of a right angle and is obtuse if its measure is greater than that of a right angle and less than a straight angle.
A reflex angle is larger than a straight angle.
→ Two intersecting lines are perpendicular if the angle between them is 90°.
→ The perpendicular bisector of a line segment is a perpendicular to the line segment that divides it into two equal parts.
→ Triangles can be classified as follows based on their angles :
| Nature of angles in the triangle | Name |
| Each angle is acute | Acute angled triangle |
| One angle is a right angle | Right angled triangle |
| One angle is obtuse | Obtuse angled triangle |
→ Triangles can be classified as follows based on the lengths of their sides :
| Nature of sides in the triangle | Name |
| All the three sides are of unequal length | Scalene triangle |
| Any two of the sides are of equal length | Isosceles triangle |
| All the three sides are of equal length | Equilateral triangle |
→ Polygons are named based on their sides.
| Number of sides | Name of the Polygon |
| 3 | Triangle |
| 4 | Quadrilateral |
| 5 | Pentagon |
| 6 | Hexagon |
| 8 | Octagon |
→ Quadrilaterals are further classified with reference to their properties.
| Properties | Name of the Quadrilateral |
| One pair of parallel sides | Trapezium |
| Two pairs of parallel sides | Parallelogram |
| Parallelogram with 4 right angles | Rectangle |
| Parallelogram with 4 sides of equal length | Rhombus |
| A rhombus with 4 right angles | Square |