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Draw a triangle ABC with side BC = 6cm, AB = 5cm and ∠ABC=60∘. Then construct a triangle whose sides are 34th of the corresponding sides of the triangle ABC.

Answer
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Hint: In this question, we are given an angle and two sides of a triangle. Firstly, we have to draw a proper triangle using given measurements and then we have to construct another triangle whose sides are 34th of corresponding sides of the previous triangle. For this, we will use a ruler, protractor and compass. We will first draw one triangle and use it to find another triangle. We will write all steps of construction.

Complete step by step answer:
Let us draw a triangle ABC with sides BC = 6cm, AB = 5cm and ∠ABC=60∘.
Following are the steps of construction to draw it.
(1): Firstly, let us draw a line segment BC of length 6cm using a ruler.
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(2): Now with B as center, let us draw an angle of 60∘ such that ∠XBC=60∘ we get,
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(3): Now with B as center and 5cm as radius on the compass, let us draw arc on the ray BX which cuts the ray BX at point A. Join A to C, we get,
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Hence ΔABC is our required triangle.
Now let us make a triangle which is 34th times the size of ΔABC. For this, following are the steps of construction.
(1): From B, let us draw any ray BX which makes same acute with side BC on the opposite to vertex A. Then let us mark 4 points B1,B2,B3,B4 on BX such that BB1=B1B2=B2B3=B3B4. For this, we shall keep the radius of the compass equal and draw the arcs.
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(1): Let us join B4 to C. Now, let us draw a line from B3 to BC which is parallel to B4C. For this, open a compass to some radius and mark angle BB4C. Keeping the same radius draws an arc from B3 which cut the line BX at some point. Then use that point at the center with radius equal to the arc on B4 to draw an arc on the previous arc. Joining this point with B3 and extending will give us a line parallel to B4C we get:
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(3): Now similarly, draw a line parallel to AC from C' to the line AB we get:
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The triangle A'C'B is our required new triangle.

Note: Students should know how to draw parallel lines, angles using compass and ruler only as they are basics for these constructions. Make sure that, pencil is sharp and the compass is tight. Draw all arcs carefully.
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