We can justify the following construction.

Draw a line segment of length 7.6 cm and divide it in the ratio 5:8. Measure the two parts. State True or False.

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True

False

answer is A.

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Detailed Solution

First of all, draw AB of length 7.6 cm:
seo

Now, draw any ray AX which makes an acute angle with AB, which means that angle should be less than 900 :
seo

Now, we are given the ratio 5 : 8 so we will mark 13 points on it as 5 + 8 = 13. So, let the 13 points will be:
A1, A2 ,A3............A13 on AX such that: AA1 = A1A2 = A2A3......... by drawing equal arcs as follows:
seo

Now, we will join BA13, which will look like the following:
seo

Since we want the ratio 5 : 8, now we will draw a line parallel to BA13. Now, we will draw a line parallel to BA13 by making ∠AA5B = ∠AA13C which we will look like the following:
seo

Thus, the ratio of AC : CB = 5 : 8, now we will measure AC and BC by the scale and we will get:
AC = 2.9 cm and BC = 4.7 cm.
Now, let’s look at the justification of this construction:
Since, ∠AA5B = ∠AA13C, therefore for lines A13B and A5C with AX as transversal, which means corresponding angles are equal.
Therefore: A13B ∥ A5B. Now, by basic proportionality theorem: