Page 1 - Lesson Note 1- ch 11 Division of line segment (Contruction)

SAI International School

CLASS - X

Mathematics
Chapter-11: Construction
Lesson Notes-1

Sub Topic: Introduction
Sub Topic: DIVISION OF LINE SEGMENT

Dividing a Line Segment

I. Bisecting a Line Segment

Step 1: Draw a line segment AB.With a radius of more than half the length of the line-segment,
draw arcs centered at either end of the line segment so that they intersect on either side of the
line segment.
Step 2: Join the points of intersection. The line segment is bisected by the line segment joining
the points of intersection.

Hence PQ is the perpendicular bisector of AB

II. Given a line segment AB, divide it in the ratio m:n, where both m and n are positive
integers.

Suppose we want to divide AB in the ratio 3:2 (m=3, n=2)
Step 1: Draw any ray AX, making an acute angle with line segment AB.

Step 2: Locate 5 (= m + n) points A1,A2,A3,A4andA5 on AX such that AA1=A1A2=A2A3=A3A4=A4A5
Step 3: Join BA5.(A(m+n)=A5)
Step 4: Through the point A3(m=3), draw a line parallel to BA5 (by making an angle equal
to ∠AA5B) at A3 intersecting AB at the point C.
Then, AC : CB = 3 : 2.

1