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Question
Draw a triangle ABC with BC = 7 cm, ∠ B = 45° and ∠C = 60°. Then construct another triangle, whose sides are `3/5` times the corresponding sides of ΔABC.
Solution
1. Draw a line BC = 7 cm.
2. Draw a ray CN making an angle of 60° at C.
3. Draw a ray BM making an angle of 45° at B.
4. Locate the point of intersection of rays CN and BM and name it as A.
5. ABC is the triangle whose similar triangle is to be drawn.
6. Draw any ray BX making an acute angle with BC on the side opposite to the vertex A.
7. Locate 5 (Greater of 3 and 5 in`3/5`) points X1, X2, X3, X4 and X5 on BX so that BX1 = X1X2 = X2X3 = X3X4 = X4 X5 .
8. Join X5C and draw a line through X3 (Smaller of 3 and 5 in`3/5`) parallel to X5C to intersect BC at C’.
9. Draw a line through C’ parallel to the line CA to intersect BA at A’.
10. A’BC’ is the required similar triangle whose sides are`3/5` times the corresponding sides of ΔABC
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