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Question -

Construct a ╬ФABC in which AB = 5 cm, тИаB = 60┬░, altitude CD = 3 cm. Construct a ╬ФAQR similar to ╬ФABC such that side of ╬ФAQR is 1.5 times that of the corresponding sides of ╬ФACB.



Answer -

Steps of construction :
(i) Draw a line segment AB = 5 cm.
(ii) At A, draw a perpendicular and cut off AE = 3 cm.
(iii) From E, draw EF || AB.
(iv) From B, draw a ray making an angle of 60 meeting EF at C.
(v) Join CA. Then ABC is the triangle.
(vi) From A, draw a ray AX making an acute angle with AB and cut off 3 equal parts making A A1= A1A2 = A2A3.
(vii) Join A2 and B.
(viii) From A , draw A^BтАЩ parallel to A2B and BтАЩCтАЩ parallel toBC.
Then ╬ФCтАЩABтАЩ is the required triangle.

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