In each of the following, give the justification of the construction also:
Draw a line segment of length 7.6 cm and divide it in the ratio 5 : 8. Measure the two parts.
Construction Procedure:
A line segment with a measure of 7.6 cm length is divided in the ratio of 5:8 as follows.
1. Draw line segment AB with the length measure of 7.6 cm
2. Draw a ray AX that makes an acute angle with line segment AB.
3. Locate the points i.e.,13 (= 5+8) points, such as A1, A2, A3, A4 …….. A13, on the ray AX such that it becomes AA1 = A1A2 = A2A3 and so on.
4. Join the line segment and the ray, BA13.
5. Through the point A5, draw a line parallel to BA13 which makes an angle equal to ∠AA13B
6. The point A5 which intersects the line AB at point C.
7. C is the point divides line segment AB of 7.6 cm in the required ratio of 5:8.
8. Now, measure the lengths of the line AC and CB. It comes out to the measure of 2.9 cm and 4.7 cm respectively.
The construction of the given problem can be justified by proving that
AC/CB = 5/ 8
By construction, we have A5C || A13B. From Basic proportionality theorem for the triangle AA13B, we get
AC/CB = AA5/A5A13….. (1)
From the figure constructed, it is observed that AA5 and A5A13 contain 5 and 8 equal divisions of line segments respectively.
AA5/A5A13 = 5/8 ….....(2)
Compare the equations (1) and (2), we obtain
AC/CB = 5/ 8