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Question 2
Construct a triangle of sides 4 cm, 5 cm and 6 cm and then a triangle similar to it whose sides are 23 of the corresponding sides of the first triangle.


Solution

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 drawn.
Step III: Again, with B as a centre and radius equal to 5 cm an arc is drawn on the same side of AB intersecting the 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.
ΔABC is the required triangle


Justification:
A(Common)
C= C' and B=  B' (corresponding angles)
Thus ΔAB'C' ~  ΔABC by AAA similarity condition
From the figure,
ABAB=AA2AA5=23
AB=23AB
AC=23AC

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