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Ex 11.1, 7 - Draw a right triangle where sides (other than hypotenuse)

Ex 11.1, 7 - Chapter 11 Class 10 Constructions - Part 2
Ex 11.1, 7 - Chapter 11 Class 10 Constructions - Part 3
Ex 11.1, 7 - Chapter 11 Class 10 Constructions - Part 4
Ex 11.1, 7 - Chapter 11 Class 10 Constructions - Part 5
Ex 11.1, 7 - Chapter 11 Class 10 Constructions - Part 6
Ex 11.1, 7 - Chapter 11 Class 10 Constructions - Part 7
Ex 11.1, 7 - Chapter 11 Class 10 Constructions - Part 8

 

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Ex 11.1, 7 Draw a right triangle in which the sides (other than hypotenuse) are of lengths 4 cm and 3 cm. Then construct another triangle whose sides are 5/3 times the corresponding sides of the given triangle First we draw a rough sketch To construct it, We follow these steps Steps to draw Δ ABC Draw base BC of side 3 cm Draw ∠ B = 90° 3. Taking B as center, 4 cm as radius, we draw an arc Let the point where arc intersects the ray be point A 4. Join AC ∴ Δ ABC is the required triangle Now, we need to make a triangle which is 5/3 times its size ∴ Scale factor = 5/3 > 1 Steps of construction Draw any ray BX making an acute angle with BC on the side opposite to the vertex A. Mark 5 (the greater of 5 and 3 in 5/3 ) points 𝐵_1, 𝐵_2, 𝐵_3,𝐵_4,𝐵_5 on BX so that 〖𝐵𝐵〗_1=𝐵_1 𝐵_2=𝐵_2 𝐵_3=𝐵_3 𝐵_4=𝐵_4 𝐵_5 Join 𝐵_3 𝐶 (3rd point as 3 is smaller in 5/3) and draw a line through 𝐵_5 parallel to 𝐵_3 𝐶, to intersect BC extended at C′. Draw a line through C′ parallel to the line AC to intersect AB extended at A′. Thus, Δ A′BC′ is the required triangle Justification Since scale factor is 5/3, we need to prove (𝑨^′ 𝑩)/𝑨𝑩=(𝑨^′ 𝑪^′)/𝑨𝑪=(𝑩𝑪^′)/𝑩𝑪 =𝟓/𝟑 By construction, BC^′/𝐵𝐶=(𝐵𝐵_5)/(𝐵𝐵_3 )=5/3 Also, A’C’ is parallel to AC So, they will make the same angle with line BC ∴ ∠ A’C’B = ∠ ACB Now, In Δ A’BC’ and Δ ABC ∠ B = ∠ B ∠ A’C’B = ∠ ACB Δ A’BC’ ∼ Δ ABC Since corresponding sides of similar triangles are in the same ratio (𝐴^′ 𝐵)/𝐴𝐵=(𝐴^′ 𝐶^′)/𝐴𝐶=(𝐵𝐶^′)/𝐵𝐶 So, (𝑨^′ 𝑩)/𝑨𝑩=(𝑨^′ 𝑪^′)/𝑨𝑪=(𝑩𝑪^′)/𝑩𝑪 =𝟓/𝟑 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.