- Geometry is the branch of mathematics that focuses on the measurement and relationship of lines, angles, surfaces, solids, and points.

# Angles

An angle is the combination of two rays with a common end-point.

- Angle is measured in degrees. A degree is denoted by °.

The types of angle are: acute angle, obtuse angle, right angle, complete angle, zero angle, reflex angle, and straight angle.

Acute Angle: An angle whose measure is less than 90 degrees but greater than 0 degrees.

Obtuse Angle: An angle whose measure is less than 180 degrees but greater than 90 degrees.

Right Angle: An angle whose measure is 90 degrees is called right angle.

Complete Angle: An angle whose measure is 360 degrees is called complete angle.

Zero Angle: If the measure of an angle is zero, its called zero angle.

Reflex Angle: An angle whose measure is greater than 180 degrees but less than 360 degrees is called reflex angle.

Straight Angle: An angle whose measure is 180 degrees is called straight angle.

Note: 360 degrees angle and 0 degree angle are different. In 360 degrees, there is one full rotation of one ray with respect to another. While in zero angle, there is no such rotation. Both rays in 0 degree angle lie on the same plane.

**Construction of a 20 degree angle using ruler and compass. **

## Lines

** SOLUTION:** Angles are= ABC, BCA, BAC, CDE, DEC, ECD, AEF, EFA, FAE

Lines are= AB, BC, CD, DE, EF, FA, AC, CE

# Circle

- A circle is a shape with all points the same distance from its centre. Area of a circle= X R
^{2}

## Triangles

- A triangle is a plane figure with three straight sides and three angles.
- On the basis of sides, triangles are classified into: Scalene (all sides are different), Isosceles (Two sides are equal), Equilateral (All sides are equal)

- On the basis of angels, triangles are divided into: acute(all angles are acute), right(one angle is 90 degree), Obtuse(one angle is obtuse), Equiangular(all angles are equal).

## Cube

- In geometry, a
*cube*is a three-dimensional solid object bounded by six square faces, sides, with three meeting at each vertex.

**EXAMPLE 1: **The radius of the circle is 3 cm. Find its diameter, circumference, and area.

**SOLUTION: **Diameter= 2 X Radius = 2 X 3 = 6 cm

Circumference= 2 X X R = 2 X X 3= 18.84 cm Area= X R^{2} = X (3)^{2}= 28.27 cm^{2}

**EXAMPLE 2: **Find the number of triangles in the following figure and name them.

** SOLUTION:**Number of triangles= 3

They are= triangle ABC, triangle CDE, triangle AEF

triangle ABC= Right angle triangle

triangle CDE= Isosceles Triangle

triangle AEF= Right Angle Triangle

# Perimeter and Area of Squares and Rectangles

- Area is a quantity that expresses the extent of a two-dimensional surface or shape in the plane.

Area of a rectangular surface= Length X Breadth units^{2}

Area of a square surface= a X a = a^{2 }units^{2}

**EXAMPLE 1: **Find the area and perimeter of a rectangle with length 1cm and breadth 2cm

**SOLUTION: **Perimeter= 2 X (Length + Breadth) = 2 X (1+2)= 6 cm

Area= Length X Breadth= 1cm X 2cm= 2cm^{2}

**EXAMPLE 2: **Find the area and perimeter of a square with side 3cm.

**SOLUTION: **Perimeter= 4 X 3 cm= 12cm

Area= 3cm X 3cm= 9cm^{2}

# Practice these questions

Q1) Name the angles.

Q2) Classify the triangles.

Q3) Find the perimeter and area of the rectangle. (Hint: Divide the irregular rectangles into two regular rectangles.)

Q4) Find the area and perimeter of the square below.

# Recap

- Only a surface can have area.
- Perimeter of rectangle= 2 X (Length + Breadth)

Perimeter of square= 4 X a - Area of rectangle= Length X Breadth

Area of square= A^{2} - Area of Circle=
- Circumference= 2 X X R
- Diameter = 2 X Radius
- There are 7 angles= acute, obtuse, reflex, complete, zero, right, and straight angle.
- On the basis of sides, there are 3 triangles= scalene, isosceles, equilateral triangle.
- On the basis of angle, there are 4 triangles = acute, obtuse, right, and equiangular triangle