In geometry, a line is a collection of points that extends indefinitely on both sides. Lines do not have a fixed length. A line segment is a part of a line. It has two end points and is of fixed length. The length of a line segment can be measured with a ruler.

**Naming the line segment**

In symbols, a line segment with two end points A and B can be written using the letters of the endpoints with a line over the letters.

**Drawing a line segment**

To draw a line segment PQ of length 7.5 cms follow the below steps:

1. Place the ruler on the paper and mark a point at 0 cms named P

2. Mark the point Q against the 7.5 cms mark on the ruler

3. Now join the points P and Q to get the line segment PQ of length 7.5 cms

**Practice examples**

Question: Draw the following line segment

1. Line segment AB of length 5.5 cms

2. Line segment PQ of length 4.8 cms

3. Line segment LM of length 8.2 cms

4. Line segment ST of length 2.5 cms

5. Line segment CD of length 6.4 cms

**Measuring the length of line segment using Pythagoras theorem**

You can also find the length of a diagonal line segment using Pythagoras theorem. Pythagoras theorem states that the square of the hypotenuse of a right angled triangle is equal to the sum of the squares of the other two sides.

In order to find the length of the diagonal line segment AB in the figure, you must first construct the right angled triangle with the line segment AB as the hypotenuse. Now applying the formula from Pythagoras theorem

Length of AB squared = Length of side 1 squared + Length of side 2 squared

= 32 + 42

= 9 + 16

= 25

Hence, length of AB = Square root of 25 = 5

**Practice questions:**

Question: Find the length of the hypotenuse of a right angled triangle of sides measuring 6 cms and 8 cms respectively (use pythagoras theorem)

( Answer: 10 cms )

Question: If the area of a square is 16 sq cms, what is the length of the line segments that make the sides of the square.

( Answer: 4 cms )

Question: Find the length of the hypotenuse of a right angled triangle of sides measuring 12 cms and 16 cms respectively (use pythagoras theorem)

( Answer: 20 cms )

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