CBSE Class 6 Maths Notes Chapter 4 Basic Geometrical Ideas PDF Download

△ABC

∠B

∠C

Quadrilaterals

A quadrilateral is a four-sided polygon, meaning that it has four sides, or line segments, and four angles as a result. For easier comprehension, a quadrilateral's diagram is provided. A quadrilateral's vertices are called in a cyclic fashion, it should be noted. AD and DC are two instances of neighbouring sides in this diagram. Moreover, AD and BC are two opposing viewpoints. Angles A and C are in opposition to one another here. The line segment in this becomes a diagonal if it is drawn from A to C or from B to D.

About Circles

A closed figure produced by a collection of points in a plane that are spaced equally apart from a fixed point that serves as the circle's centre is known as a circle. Several key phrases associated with circles are:

Terms	Definitions
Radius	The fixed distance at which the points are located from the centre is called the radius.
Diameter	Diameter is the length of a line segment which joins any two points on the circle by passing through the centre. Diameter is always double than the radius.
Circumference	The distance around the circle is known as its circumference or perimeter.
Chord	A line segment joining any two points on the circle is a chord.
Sector	It is the region in the interior of a circle which is enclosed by an arc on one side and a pair of radii on the other two sides.
Segment	It is a region in the interior of the circle enclosed by an arc and a chord.

Points

• A point determines a specific location.
• They are denoted by any capital letter of the English Alphabet.

Curves

• In simple terms, any line that is not straight is said to be a curve.
• If a curve does not cross itself, then it is called a simple curve.

Closed and Open Curves

If the ends of a curve are connected, it is considered closed. An open curve is defined as one whose endpoints are open.

Polygons

A simple closed figure made up of line segments is called a polygon.

Terms Related to Polygons

Some of the important terms related to a polygon are :

• Vertex: The meeting point of a pair of sides. Here A, B, C, D and E are the vertices of the polygon.
• Adjacent sides: Any two sides of a polygon with a common endpoint. Here AB and BC are adjacent sides.
• Adjacent vertices: Endpoints of the same side of a polygon. Here A and B are the adjacent vertices.
• Diagonals: The lines joining the non-adjacent vertices of a polygon. Here AC, AD, BD, BE and CE are the diagonals.

Triangle

A polygon with three sides is a triangle. It is composed of three vertices, three angles, and three sides. It consists of an outside and an inside zone. In the above figure:

Quadrilaterals

A polygon with four sides, four angles, and four vertices is called a quadrilateral. In a quadrilateral ABCD:

• AB, BC, CD and DA are the sides of the quadrilateral.
• A, B, C and D are the vertices.
• AB and CD, and BC and DA are the pairs of opposite sides.
• Angle A and angle C, and angles B and D are the pairs of opposite angles.
• Angle A is adjacent to angle B and angle D. Similar relations exist for all other angles.

Angles

Two rays that begin at the same endpoint form an angle. We refer to these rays as the angle's arms. The vertex of the angle is the name given to the shared terminal. The angle's vertex must be in the centre when designating the angle. Ray OP and Ray OQ, for instance, make an angle. It has the symbol ∠POQ. Ray OP and OQ are the arms or sides of the angle. O is the vertex of the angle POQ

Exterior and Interior Points to an Angle

Its plane is divided into three sections by an angle. The angles, their interiors, and their exteriors are these places. In the figure above, points F and R lie in the interior of ∠ABC. Points A, B and C lie on the angle ∠ABC and P, X, and T lie on the exterior of angle ∠ABC.

Circles

A circle isn't a polygon; it's just a straightforward closed curve. In essence, a circle is created when a point moves away from a fixed point at a defined distance. The centre is this fixed location in the middle. The circumference is the distance a point travels around a circle.

Terms Related to Circle

A line segment connecting any two points on a circle is called its chord. A diameter is a chord that goes through a circle's centre. A circle's diameter splits it into two equal parts, known as semicircles. A sector is an area inside a circle that is bounded by two radii on two of its sides and an arc on one of its sides. A segment is an area inside a circle that is bounded by an arc and a chord.

All About Lines

Line Segment

Lines

A line segment is defined as one that can be infinitely extended on both sides. This is a line, m. It has an endless amount of points on it.

Ray

A segment of a line is called a ray. It begins at what is known as its starting point and continues indefinitely in the opposite direction.

Intersecting and Parallel Lines

Two lines are said to intersect when they share a point. Since lines l and m in this instance share a point P, they intersect at P, which serves as the intersection point. Two lines are considered parallel if they do not share a point. Here, the lines AB and CD are parallel.

Position in a Figure

The components of a closed curve are threefold. In the following figure, N is outside the curve, M is on the border, and L is inside the curve. The region of a curve is the inside of the curve plus its boundary.