Basic Geometrical Ideas Class 6 Maths NCERT Chapter 4

Key Features of NCERT Material for Class 6 Maths Chapter 4 – Basic Geometrical Ideas 

In the previous chapter3 of NCERT class 4, you studied the numbers., types of numbers and properties for numbers. In this chapter of class 6 maths: Basic Geometrical Ideas, you will study Lines, line segments, angles, polygons, quadrilaterals, curves, triangles and circles.

Quick revision notes

The term ‘Geometry‘ is what could be compared to the Greek word ‘Geometron’. ‘Geo’ means Earth and ‘metron’ means Measurement. Geometrical thoughts are reflected in infill types of art, measurements, architecture, engineering, and so forth. We observe and utilize various articles. These items have various shapes. The ruler is straight while a ball is round. In this part, we will gain proficiency with some fascinating realities which enable us to find out about the shapes around us. 

Let’s mark a dot on the paper by a sharp tip of the pencil. More keen the tip, more thinner will be the dot. This almost undetectable more thinner dot gives us a thought of a point. A point decides an area. Coming up next are a few models for a point. 

Line Segment 

The shortest join of two points is a line segment. The line segment joining two points A and B is indicated by or . The points A and B are known as endpoints of the segment. 

Note: and indicate the same line segment.

Line 

A line is obtained when a line segment like  is reached out on the two sides indefinitely. It is represented by . In some cases, it is indicated by a single letter like l. Albeit a line contains an innumerable number of points, yet two points are sufficient to determine a line. We state ‘two points determine a line.’ 

Intersecting Lines 

Two lines are called intersecting lines when they have one point in common. 

Parallel Lines 

Two lines in a plane are supposed to be parallel lines if they don’t intersect. 

Ray

A ray is a segment of a line. It begins at a certain point (called starting point) and goes infinitely in one direction. 

Curves

Any drawing (straight or non-straight) drawn without lifting the pencil from the paper and without the utilization of a ruler is known as a curve. In regular use curve signifies ‘not straight’ yet in mathematics, a curve can be a straight line as well. A curve is known as a simple curve when it does not cross itself. A curve is supposed to be a close curve if its ends are joined; else, it is called an open curve. 

A closed curve has three disjoint parts as follows: 

• Interior
• Boundary
• Exterior

The interior of a curve along with its boundary is called its region. 

Polygons 

A closed curve totally made of line segments is called a polygon. The line segments framing a polygon are known as its sides. The meeting point of a pair of sides is known as its vertex. Any two different sides with a common endpoint are known as the adjacent sides. The endpoints of a side are known as the adjacent vertices. The join of any two non-adjacent vertices is known as a diagonal of the polygon. 

Angles

An angle is comprised of two rays beginning from a common endpoint. Two rays OP and OQ beginning from the common endpoint O form ∠POQ ( (or additionally called ∠QOP) at O. Point O is known as the vertex of ∠POQ. Rays OP and OQ form two different sides of ∠POQ. Note that in indicating an edge, the vertex is always written as the centre letter. 

An angle prompts three divisions of a region: 

• On the angle
• The interior of the angle
• The exterior of the angle.

Triangles 

A triangle is a polygon with 3 sides. Actually, it is a polygon with a minimal number of sides. Triangle ABC is composed as ∆ABC. There are three sides to a triangle. So, the sides of ∆ABC are  , and  . A triangle has 3 angles. In this way, the angles of ∆ABC are ∠BAC, ∠ABC, and ∠BCA. The points A, B, and C are known as the vertices of the triangle ABC. Like angle, a triangle likewise has three regions related to it.

• On the triangle
• The interior of the triangle
• The exterior of the triangle.

Quadrilaterals 

A quadrilateral is a polygon with four sides. It has four sides and four angles. A quadrilateral has 4 vertices which ought to be named cyclically. 

In the quadrilateral ABCD, the four sides are , ,and ;While four angles are ∠A, ∠B, ∠C & ∠D 

Adjacent sides are , ; [latex1]\bar { BC }[/latex],; , ; , . 

Pair of opposite sides are and ; and .

Pair of opposite angles are ∠A & ∠C; ∠B & ∠D

And adjacent angles are ∠A & ∠B; ∠B & ∠C; ∠C & ∠D; ∠D & ∠A

Circle 

A circle is a path of a point moving at an equal distance from a fixed point. The fixed point is known as the centre, the fixed distance is known as the radius and the distance around the circle is known as the circumference. A line segment joining any two points on the circumference is called a chord of the circle. A diameter is a chord going through the centre. A diameter is twofold the size of a radius. Any diameter of a circle separates it into two semi-circles. An arc is any part of a circle. For two points P and Q on the circle, we get the arc, denoted as PQ. Like a simple closed curve, three regions are associated with a curve are as follows;

• On the circle
• The interior of the circle
• The exterior of the circle.