Q4 of 805 Page 13

Construct a ΔABC in which BC = 5 cm, ∠C = 60° and altitude from A equal to 3 cm. Construct a ΔADE similar to ΔABC such that each side of Δ ADE is times the corresponding side of ΔABC. Write the steps of construction.


Steps of Construction:


1. Draw a line segment BC = 5 cm.



2. Draw ∠ ECB = 60°.



3. Draw a line parallel to BC at a distance of 3 cm. Let it intersect EC at A.



4. Join AB.



5. Δ ABC is the required triangle.


6. Draw a ray BX on the side opposite to the vertex A. Also, ∠ CBX should be acute.



7. Along BX, mark 3 points C1, C2, C3 such that BC1 = C1C2 = C2C3.



8. Join C2C.



9. Draw C3C’ parallel to C2C such that C’ lies on the extended line BC.



10. Draw C’A’ parallel to AC such that A’ lies on extended BA.



Δ A’BC’ is the required triangle whose sides are times the sides of Δ ABC.


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