Chapter 11 : Constructions
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go Exercise 11.1
follow url 1. 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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write my eassy Steps of Construction:
research paper Step I: AB = 7.6 cm is drawn.
Step II: A ray AX making an acute angle with AB is drawn.
Step III: After that, a ray BY is drawn parallel to AX making equal acute angle as in the previous step.
follow url Step IV: Point A1, A2, A3, A4 and A5 is marked on AX and point B1, B2…. to B8 is marked on BY such that AA1 = A1A2 = A2A3 =….BB1= B1B2 = …. B7B8
Step V: A5 and B8 is joined and it intersected AB at point C diving it in the ratio 5:8.
AC : CB = 5 : 8
ΔAA5C ~ ΔBB8C
∴ AA5/BB8 = AC/BC = 5/8
2. Construct a triangle of sides 4 cm, 5 cm and 6 cm and then a triangle similar to it whose sides are 2/3 of the corresponding sides of the first triangle.
Steps of Construction:
Step I: AB = 6 cm is drawn.
Step II: With A as a centre and radius equal to 4 cm, an arc is draw.
Step III: Again, with B as a centre and radius equal to 5 cm an arc is drawn on same side of AB intersecting previous arc at C.
Step IV: AC and BC are joined to form ΔABC.
Step V: A ray AX is drawn making an acute angle with AB below it.
Step VI: 5 equal points (sum of the ratio = 2 + 3 =5) is marked on AX as A1 A2….A5
Step VII: A5B is joined. A2B’ is drawn parallel to A5B and B’C’ is drawn parallel to BC.
ΔAB’C’ is the required triangle
∠C = ∠C’ and ∠B = ∠ B’ (corresponding angles)
Thus ΔAB’C’ ~ ΔABC by AAA similarity condition
From the figure,
AB’/AB = AA2/AA5 = 2/3
AB’ =2/3 AB
AC’ = 2/3 AC