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.
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. 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, AB′AB=AA2AA5=23 AB′=23AB AC′=23AC