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Q.1In each of the following, give the justification of the construction also: 1. Draw a line segment of length 7.6 cm and divide it in the ratio 5 : 8. Measure the two parts.

Steps of construction:

(1) Draw a line segment AB = 7cm.
(2) Draw an acute angle BAX on base AB. Mark the ray AX.
(3) Locate 13 point A1, A2, A3........A13 on the ray AX so that AA1=A1A2=A2A3........
(4) join A13 with B and A5 draw a line || to BA3 that is A5C . The line intersects AB at C .
(5) On measure AC = 2.9 cm and BC = 4.7 cm

justification:

In triangle AA5C and triangle AA13B
A5C || A13B
$$\frac{AC}{BC} = \frac{AA5}{A5A13} = \frac{5}{8}$$
$$\therefore$$ AC : BC = 5:8