Construct a triangle of sides 4 cm, 5 cm and 6 cm and then a triangle similar to it whose sides are 2/3 of the corresponding sides of the first triangle.
Question
Construct a triangle of sides 4 cm, 5 cm and 6 cm and then a triangle similar to it whose sides are 2/3 of the corresponding sides of the first triangle.
Solution
Sure, here are the steps to construct the triangles:
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Draw a line segment AB of 4 cm.
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With A as center and radius 5 cm, draw an arc.
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With B as center and radius 6 cm, draw another arc intersecting the first arc at point C.
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Join AC and BC to form the triangle ABC.
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Now, to construct a triangle similar to ABC with sides 2/3 of the original, draw a line segment DE of length 2/3 * 4 cm = 2.67 cm.
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With D as center and radius 2/3 * 5 cm = 3.33 cm, draw an arc.
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With E as center and radius 2/3 * 6 cm = 4 cm, draw another arc intersecting the first arc at point F.
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Join DF and EF to form the triangle DEF.
Now, triangle DEF is similar to triangle ABC and its sides are 2/3 of the corresponding sides of triangle ABC.
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