Example 1 - Construct a triangle similar to triangle ABC with its side

Example 1 - Chapter 11 Class 10 Constructions - Part 2
Example 1 - Chapter 11 Class 10 Constructions - Part 3 Example 1 - Chapter 11 Class 10 Constructions - Part 4 Example 1 - Chapter 11 Class 10 Constructions - Part 5

 

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Example 1 Construct a triangle similar to a given triangle ABC with its sides equal to 3/4 of the corresponding sides of the triangle ABC (i.e. of scale factor 3/4). Here, we are given Ξ” ABC, and scale factor 3/4 ∴ Scale Factor < 1 We need to construct triangle similar to Ξ” ABC Let’s follow these steps Steps of construction Draw any ray BX making an acute angle with BC on the side opposite to the vertex A. Mark 4 (the greater of 3 and 4 in 3/4 ) points 𝐡_1,𝐡_2,𝐡_3 and 𝐡_4 on BX so that 〖𝐡𝐡〗_1=𝐡_1 𝐡_2=𝐡_2 𝐡_3=𝐡_3 𝐡_4. Join 𝐡_4C and draw a line through 𝐡_3 (the 3rd point, 3 being smaller of 3 and 4 in 3/4) parallel to 𝐡_4 𝐢, to intersect BC at Cβ€². 4. Draw a line through Cβ€² parallel to the line CA to intersect BA at Aβ€². Thus, Ξ” Aβ€²BCβ€² is the required triangle Justification Since scale factor is 3/4, we need to prove (𝑨^β€² 𝑩)/𝑨𝑩=(𝑨^β€² π‘ͺ^β€²)/𝑨π‘ͺ=(𝑩π‘ͺ^β€²)/𝑩π‘ͺ =πŸ‘/πŸ’. By construction, BC^β€²/𝐡𝐢=(𝐡𝐡_3)/(𝐡𝐡_4 )=3/4. Also, A’C’ is parallel to AC So, they will make the same angle with line BC ∴ ∠ A’C’B = ∠ ACB Now, In Ξ” A’BC’ and Ξ” ABC ∠ B = ∠ B ∠ A’C’B = ∠ ACB Ξ” A’BC’ ∼ Ξ” ABC Since corresponding sides of similar triangles are in the same ratio (𝐴^β€² 𝐡)/𝐴𝐡=(𝐴^β€² 𝐢^β€²)/𝐴𝐢=(𝐡𝐢^β€²)/𝐡𝐢 So, (𝑨^β€² 𝑩)/𝑨𝑩=(𝑨^β€² π‘ͺ^β€²)/𝑨π‘ͺ=(𝑩π‘ͺ^β€²)/𝑩π‘ͺ =πŸ‘/πŸ’. Thus, our construction is justified

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.