Q. 124.2( 5 Votes )
Step 1. At first drawn a base line BC of length 5.5 cm with the help of scale.
Step 2. Taking B as center draw an arc of radius 5 cm with the help of compass. Similarly taking C as center draw a arc of radius 6.5 cm with the help of compass.
Join AB and AC thus completing the triangle ABC.
Step 3. A ray BX is drawn making an acute angle with BC opposite to vertex A. Five points B1 , B2 , B3, B4, and B5 at equal distance is marked on BX.
Step 4. B3 is joined with C to form B3 C as 3 point is smaller. B5 C1 is drawn parallel to B3 C as 5 point is greater.
Step 5:C1A1is drawn parallel to CA.
Thus, A1BC1 is the required triangle.
Since the scale factor is ,
We need to prove,
Also, A1C1 is parallel to AC.
So, this will make same angle with BC.
∴ ∠A1C1B = ∠ACB …. (2)
In ΔA1BC1 and ΔABC
∠ B = ∠ B (common)
∠A1C1B = ∠ACB (from 2)
Since corresponding sides of similar triangles are in same ratio.
Hence construction is justified.
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