As a continuation from your previous class, students now are introduced to construct several other geometrical figures and also given their justification. This exercise deals with problems to understand and construct the division of a line segment. Students can refer the RD Sharma Solutions Class 10 for getting a clear idea of how the answers are to be presented in their exams. Further, students can also download the RD Sharma Solutions for Class 10 Maths Chapter 11 Constructions Exercise 11.1 PDF provided below for reference.
Access RD Sharma Solutions for Class 10 Chapter 11 Constructions Exercise 11.1
1. Determine a point which divides a line segment of length 12 cm internally in the ratio of 2: 3. Also, justify your construction.
Steps of construction:
1. Draw a line segment AB = 12 cm by using a ruler.
2. Through the points A and B draw two parallel line on the opposite side of AB and making the same acute angles with the line segment.
3. Cut 2 equal parts on AX and 3 equal parts on BY such that AX1 = X1X2 and BY1 = Y1Y2 = Y2Y3.
4. Join X2Y3 which intersects AB at P
Hence, AP/PB = 2/3.
In ΔAX2P and ΔBY3P, we have
∠APX2 = ∠BPY3 [vertically opposite angle]
∠X2AP = ∠Y3BP [alternate interior angles}
ΔAX2P ΔBY3P [Because AA similarity]
∴ AP/BP = AX2/BY3 = 2/3 [From C.P.C.T]