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Ex 11.1, 3 - Construct a triangle with sides 5 cm, 6 cm and 7 cm

Ex 11.1, 3 - Chapter 11 Class 10 Constructions - Part 2
Ex 11.1, 3 - Chapter 11 Class 10 Constructions - Part 3
Ex 11.1, 3 - Chapter 11 Class 10 Constructions - Part 4
Ex 11.1, 3 - Chapter 11 Class 10 Constructions - Part 5
Ex 11.1, 3 - Chapter 11 Class 10 Constructions - Part 6
Ex 11.1, 3 - Chapter 11 Class 10 Constructions - Part 7

 

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Ex 11.1, 3 Construct a triangle with sides 5 cm, 6 cm and 7 cm and then another triangle whose sides are 7/5 of the corresponding sides of the first triangle. Let’s first construct Δ ABC with sides 5 cm, 6 cm, 7 cm Steps to draw Δ ABC Draw base AB of side 5 cm With A as center, and 6 cm as radius, draw an arc With B as center, and 7 cm as radius, draw an arc 3. Let C be the point where the two arcs intersect. Join AC & BC Thus, Δ ABC is the required triangle Now, let’s make a similar triangle with Scale factor = 7/5 Steps of construction Draw any ray AX making an acute angle with AB on the side opposite to the vertex C. Mark 7 (the greater of 7 and 5 in 7/5 ) points 𝐴_1, 𝐴_2, 𝐴_3, 𝐴_4, 𝐴_5, 𝐴_6, 𝐴_7 on AX so that 〖𝐴𝐴〗_1=𝐴_1 𝐴_2=𝐴_2 𝐴_3 … and so on Join 𝐴_5 𝐵 (5th point as 5 is smaller in 7/5) and draw a line through 𝐴_7 parallel to 𝐴_5 𝐵, to intersect AB extended at B′. Draw a line through B′ parallel to the line BC to intersect AC extended at C′. Thus, Δ AB’C′ is the required triangle Justification Since scale factor is 7/5, we need to prove (𝑨𝑩^′)/𝑨𝑩=(𝑨𝑪^′)/𝑨𝑪=(𝑩^′ 𝑪^′)/𝑩𝑪 = 𝟕/𝟓 By construction, (𝐴B^′)/𝐴𝐵=(𝐴𝐴_7)/(𝐴𝐴_5 )= 7/5 Also, B’C’ is parallel to BC So, the will make the same angle with line AB ∴ ∠ AB’C’ = ∠ ABC Now, In Δ AB’C’ and Δ ABC ∠ A = ∠ A ∠ AB’C’ = ∠ ABC Δ AB’C’ ∼ Δ ABC Since corresponding sides of similar triangles are in the same ratio (𝐴𝐵^′)/𝐴𝐵=(𝐴𝐶^′)/𝐴𝐶=(𝐵^′ 𝐶^′)/𝐵𝐶 So,(𝑨𝑩^′)/𝑨𝑩=(𝑨𝑪^′)/𝑨𝑪=(𝑩^′ 𝑪^′)/𝑩𝑪 =𝟕/𝟓. Thus, our construction is justified

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.