Q. 325.0( 4 Votes )

# 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.

fig.25

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

fig.26

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

fig.27

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′.

fig.28

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

fig.29

Then ABC is the required triangle.

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