5th Class Mathematics Geometry

Geometry

Category : 5th Class

Geometry

Line:

A group of points in a straight path, extending on both sides infinitely form a line. Two points on the line denote it.

A line \[\overleftrightarrow{\text{AB}}\] is read as line AB'.

\[\overleftrightarrow{\text{AB}}\]=\[\overleftrightarrow{\text{BA}}\]

Line Segment:

A part of a line with two end points is called a line segment. It has a definite length.

Line segment

A line segment PQ is written as PQ.

\[\overline{\text{PQ }}\text{= }\overline{\text{QP}}\]

Ray:

A part of a line, which extends infinitely in one direction only, from a point, is a ray. The point is called the end-point of the ray.

A ray OP is written as 0?. A ray is denoted by writing the initial point first.

So, \[\overrightarrow{\text{OP}}\ne \overrightarrow{\text{PO}\text{.}}\]

Angle:

Two rays or line segments with a common end-point form an angle.

The common end-point is called the vertex of the angle and rays or line segments are called arms of the angle.

The unit of the angle is degree denoted by a small ° on the measure.

e.g., \[\angle \text{AOB}\]=47°

\[\overrightarrow{\text{OA}}\] and \[\overrightarrow{\text{OB}}\] form an angle AOB. 0 is the vertex of \[\angle \text{AOB}\]and \[\overrightarrow{\text{OA}}\]and \[\overrightarrow{\text{OB}}\] are its arms or sides.

Z AOB is the same as Z BOA. Only vertex can also be used to denote an angle. Thus ZA means the angle whose vertex is A.

Types of Angles:

(a) An angle whose measure is between 0° and 90° is called an acute angle.

(b) An angle whose measure is 90° is called a right angle.

Collinear Points: The points which lie on the same line, are called collinear points.
Non-collinear points: The points which do not lie on the same line are called non-collinear points.

In the given figure, B, F, and E are collinear, while A, C and D are non-collinear points.

Circle: The set of points equidistant from a fixed point is called a circle. The fixed point is called the centre of the circle.

The centre of a circle is usually denoted as 0.

Radius: The distance between the centre and any point on the circle is called the radius. All the radii of the same circle have the same length. Infinitely many radii can be drawn in a circle.

In the figure, OA = OC = OD = radius

Diameter: A line segment that passes through the center of the circle and whose end-points lie on the circle is called a diameter. In the figure, CD is a diameter.

Diameter = 2 x Radius

All the diameters of a circle are of the same lengths.

Infinitely many diameters can be drawn in a circle.

Chord: A line segment which joins two points on the circumference of a circle is called a chord of the circle. A diameter is the longest chord of a circle.
Arc: Any part of the circumference of a circle is called an arc.
Semicircle: Half of the circumference of a circle is called a semicircle.
Triangle: A closed figure formed by three line segments is called a triangle. A triangle is named using its vertices A, B, and C. It is denoted as AABC, read as triangle ABC.