Q. 33.9( 18 Votes )

Construct a triangle of sides 4 cm, 5 cm and 6 cm and then a triangle similar to it whose sides are (2/5) of the corresponding sides of it.

Answer :

Steps of Construction:


Step I: AB = 6 cm is drawn.



Step II: With A as a centre and radius equal to 4cm, an arc is draw. 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 III: AC and BC are joined to form ΔABC.



Step IV: A ray AX is drawn making an acute angle with AB below it.



Step V: 5 equal points (sum of the ratio = 2 + 3 =5) is marked on AX as A1 A2....A5



Step VI: A5B is joined. A2 B' is drawn parallel to A5B and B'C' is drawn parallel to BC.


ΔAB'C' 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,





Hence Proved.


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