Construct a ΔABC in which BC = 5.4 cm, AB = 4.5 cm and ∠ ABC = 60˚.

Construct a triangle similar to this triangle, whose side are 3/4 of the corresponding sides of ΔABC.

Steps of Construction :


1. Draw a line Segment BC = 5.4 cm and draw an angle of 60°


at point B and mark a length of AB = 4.5 cm on the line passing through B. Then join AC.


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2. Draw any ray BX making an acute angle with BC on the side opposite to the vertex A.


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3. Locate 4 points [the greater of 4 and 3 in (3/4)] B1, B2, B3, B4 on BX so that


BB1 = B1B2 = B2B3 = B3B4


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4. Join B3 [the 3rd point, 3 being smaller of 3 and 4 in (3/4)] to C and draw a line through B4 parallel to B3C, intersecting the extended line segment BC at C′.


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5. Draw a line through C′ parallel to CA intersecting the extended line segment BA at A′.


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Then A′BC′ is the required triangle.


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