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Construct a Triangle Similar to a Given δAbc Such that Each of Its Sides is (5/7)Th of the Corresponding Sides of δ Abc. It is Given that Ab = 5 Cm, Bc = 7 Cm and ∠Abc = 50°. - Mathematics

Construct a triangle similar to a given ΔABC such that each of its sides is (5/7)th  of the corresponding sides of Δ ABC. It is given that AB = 5 cm, BC = 7 cm and ∠ABC = 50°.

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Solution

Given that

AB = 5 cm, BC = 7 cm and ∠ABC = 50°

Construct a triangle similar to a triangle ABC such that each of sides is (5/7)th of the corresponding sides of triangle ABC.

We follow the following steps to construct the given

Step of construction

Step: I- First of all we draw a line segment AB = 5 cm.

Step: II- With as centre and draw an angle ∠ABY = 50°.

Step: III- With as centre and radius = BC = 7 cm, draw an arc, cut the line BY drawn in step II at C.

Step: IV- Joins AC to obtain ΔABC.

Step: V- Below AB, makes an acute angle ∠BAX = 60°.

Step: VI- Along AX, mark off seven points A1, A2, A3, A4, A5, A6 and A7 such that AA1 = A1A2 = A2A3 = A3A4 = A4A5 = A5A6 = A6A7

Step: VII-Join A7B.

Step: VIII- Since we have to construct a triangle each of whose sides is (5/7)th of the corresponding sides of ΔABC.

So, we take five parts out of seven equal parts on AX from point A5 draw A5B' || A7B and meeting AB at B’.

Step: IX- From B'draw B'C || BC and meeting AC at C’

Thus, ΔAB'C' is the required triangle, each of whose sides is (5/7)th of the corresponding sides of ΔABC.

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APPEARS IN

RD Sharma Class 10 Maths
Chapter 9 Constructions
Exercise 9.2 | Q 2 | Page 9
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