Ex 11.1, 5 - Draw a triangle ABC with side BC = 6 cm, AB = 5 cm, angle

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

 

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Question 5 Draw a triangle ABC with side BC = 6 cm, AB = 5 cm and ∠ ABC = 60°. Then construct a triangle whose sides are 3/4 of the corresponding sides of the triangle ABC. Let’s first draw a rough diagram Now, Let’s construct it Steps to draw Δ ABC Draw base BC of side 6 cm Draw ∠ B = 60° Note: To learn how to draw 60°, check Construction 11.1 of Class 9 3. Taking B as center, 5 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 3/4 times its size ∴ Scale factor = 3/4 < 1 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 𝐵_1, 𝐵_2, 𝐵_3,𝐵_4 on BX so that 〖𝐵𝐵〗_1=𝐵_1 𝐵_2=𝐵_2 𝐵_3=𝐵_3 𝐵_4 Join 𝐵_4 𝐶 and draw a line through 𝐵_3 (the 3rd point, 3 being smaller of 3 and 4 in 3/4) parallel to 𝐵_4 𝐶, to intersect BC at C′. 4. Draw a line through C′ parallel to the line AC to intersect BA at A′. Thus, Δ A’BC′ is the required triangle Justification Since scale factor is 3/4, we need to prove (𝑨^′ 𝑩)/𝑨𝑩=(𝑨^′ 𝑪^′)/𝑨𝑪=(𝑩𝑪^′)/𝑩𝑪 =𝟑/𝟒. By construction, BC^′/𝐵𝐶=(𝐵𝐵_3)/(𝐵𝐵_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 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 =𝟑/𝟒. 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.