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# Draw a line segment of length 7.6 cm and divide it in the ratio 5 : 8. Measure the two parts Q.1

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How i draw a line segment type question form class 10th ncert book of class 10th of chapter constructions of exercise 11.1, give me the best and easy way to draw this question Draw a line segment of length 7.6 cm and divide it in the ratio 5 : 8. Measure the two parts

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1. 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 â€¦â€¦.. 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 âˆ 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.

Justification:

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/A5A13â€¦.. (1)

From the figure constructed, it is observed that AA5 and A5A13 contain 5 and 8 equal divisions of line segments respectively.

Therefore, it becomes

AA5/A5A13=5/8â€¦ (2)

Compare the equations (1) and (2), we obtain

AC/CB = 5/ 8

Hence, Justified.

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