Geometry for grade  7.

Line / Ray / Line segment:

A Line segment has fixed length, a ray has fixed length from on side and can be extended from another side and a line has no fixed end point and it can be extended on both sides.

Point of intersection:

When two lines  (rays or line segments ) cut each other then the point on which they cut is known as point of intersection. O is point of intersection in the given diagram,

                                                            

Measuring an angle:

We can measure the angles. Just like we measure lengths of lines etc. Angles are measured in degrees. The symbol used for degree is a small circle. A circle is divided in 360^o degrees. Half of the circle is 180^o degrees. That is a straight line is 180^o degrees. The instrument use to measure the degrees of an angle is called “D” because it shapes like the letter D.

Types of the angles:

Depending on the types of degrees of the angles, we can divide them in different types. They are:

1.      Right angles.

2.      Acute angles.

3.      Obtuse angles.

Right angle:

An angle of 90^o degree is called a right angle. It is ¼ the of a circle. The right angle is mostly marked with a small square.

Acute angle: 

An angle less than 90^o degrees is called an acute angle. 

Obtuse angle:

An angle greater than 90^o degrees is called obtuse angle.

Angle addition:

We can also add the triangles.

For example:

If we add two angles one of 45^o degrees and the other of 30^o degrees than we will get an angle of:

 45^o + 30^o = 75^o degrees.

Types of pairs of angles:

Depending on the sum of angles we divide them as:

1.      Complementary angles.

If the sum of two angles is 90^o degrees we call them complementary angles. In this case on angle is called the complement of the other.

If we do not know the complement of one angle we can find it by subtracting the angle from 90^o.

What will be the complement of 45^o?

The complement of 45^o degree angle is 

= 90^o – 45^o = 45^o degree.

2.      Supplementary angles.

When the sum of two angles is 180^o degrees then we call them supplement angles. In this case one angle is called the supplement of the other.

Supplement of an angle of degree 95^o is 85^o and the angle thus formed is called supplementary angle because 95^o + 85^o = 180^o. We can find the supplement of an angle if we subtract it from 180^o.

What is the supplement of <120^o ?

180^o – 120^o = 40^o,the supplement of 120^o is 40^o.

Triangles:

A triangle is closed shape which has three angles and three sides. Different figures of triangles are as follows:

Classification of triangles with respect to sides.

§         Equilateral Triangle.

This triangle all has three sides of equal length. Figure shows an equilateral triangle,

 

§         Scalene Triangle.

This triangle has none of  its sides of equal length.

 

§         Isosceles Triangle.

This triangle has two of its sides of equal length.

                         

Classification of triangles with respect to angles:

§         Right-angled triangle.

A triangle which

§         Obtuse-angled triangle.

§         Acute-angled triangle.

Back