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Question

Draw an isosceles ΔABC in which BC=5.5cm and altitude AL=3 cm. Then construct another triangle whose sides are 34 of the corresponding sides of ΔABC.


Solution

Steps of construction:

(i) Draw a line segment BC=5.5 cm.

(ii) Draw a perpendicular bisector of BC intersecting



BC at L such that AL=3 cm.

(iii) Join AB and AC

Thus, ΔABC is obtained.

(iv) Below BC, make an acute angle CBX.

(v) Along BX, mark off four points B1, B2, B3, B4

such that BB1=B1B2=B2B3=B3B4.

(vi) Join B4C.

(vii) From B3 draw B3D || B4C, meeting BC at D.

(viii) From D, draw DE || CA, meeting AB at E.

Then ΔEBD is the required triangle each of whose

sides is 34 of the corresponding side of ΔABC.

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