Draw a line segment length 7.6 cm and divide it in the ratio 5 : 8. Measure the two parts. Give the justification of the construction.

Steps of construction:

Draw line AB of length 7.6 cm

Draw any ray AX, making an acute angle (angle less than 90°) with AB.

Mark 13 (= 5 + 8) points, A_1, (A)_2, A_3, A_4……. A_13, on AX such that (AA)_1=A_1 A_2=A_2 A_3 and so on.

Join (BA)_13.

Since we want the ratio 5 : 8, Through point A_5 (m = 5), we draw a line parallel to (BA)_13(by making an angle equal to ∠AA13B at A5) intersecting AB at the point C.

Ex 11.1, 1
Draw a line segment length 7.6 cm and divide it in the ratio 5 : 8. Measure the two parts. Give the justification of the construction.
Steps of construction:
Draw line AB of length 7.6 cm
Draw any ray AX, making an acute angle (angle less than 90°) with AB.
Mark 13 (= 5 + 8) points, A_1, (A)_2, A_3, A_4……. A_13, on AX such that (AA)_1=A_1 A_2=A_2 A_3 and so on.
Join (BA)_13.
Since we want the ratio 5 : 8, Through point A_5 (m = 5), we draw a line parallel to (BA)_13(by making an angle equal to ∠AA13B at A5) intersecting AB at the point C.
Then, AC : CB = 5 : 8.
Measuring by scale,
AC = 2.9 cm and BC = 4.7 cm
Justification
In Δ AA13B
Since A_3 C is parallel to A_5 B, therefore,
(AA)_5/(A_5 A_13 )=AC/CB
By construction, (AA)_3/(A_3 A_5 )=5/8.
Therefore, AC/CB=5/8.
This shows that C divides AB in the ratio 5 : 8.