Constructions
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Ex 11.1, 2 - Construct a triangle of sides 4 cm, 5 cm and 6 cm

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

 

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Question 2 Construct a triangle of sides 4 cm, 5 cm and 6 cm and then a triangle similar to it whose sides are 2/3 of the corresponding sides of the first triangle. Let’s first construct Δ ABC with sides 4 cm, 5 cm, 6 cm Steps to draw Δ ABC Draw base AB of side 4 cm With A as center, and 5 cm as radius, draw an arc With B as center, and 6 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 = 2/3 Steps of construction Draw any ray AX making an acute angle with AB on the side opposite to the vertex C. Mark 3 (the greater of 2 and 3 in 2/3 ) points 𝐴_1, 𝐴_2, 𝐴_3 on AX so that 〖𝐴𝐴〗_1=𝐴_1 𝐴_2=𝐴_2 𝐴_3 Join 𝐴_3B and draw a line through 𝐴_2 (the 2nd point, 2 being smaller of 2 and 3 in 2/3) parallel to 𝐴_3 𝐵, to intersect AB at B′. 4. Draw a line through B′ parallel to the line BC to intersect AC at C′. Thus, Δ AB’C′ is the required triangle Justification Since scale factor is 2/3, we need to prove (𝑨𝑩^′)/𝑨𝑩=(𝑨𝑪^′)/𝑨𝑪=(𝑩^′ 𝑪^′)/𝑩𝑪 = 𝟐/𝟑 By construction, (𝐴B^′)/𝐴𝐵=(𝐴𝐴_2)/(𝐴𝐴_3 )= 2/3 Also, B’C’ is parallel to BC So, the will make the same angle with line AB ∴ ∠ AB’C’ = ∠ ABC (Corresponding angles) Now, In Δ AB’C’ and Δ ABC ∠ A = ∠ A (Common) ∠ AB’C’ = ∠ ABC (From (2)) Δ AB’C’ ∼ Δ ABC (AA Similarity) 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 =𝟐/𝟑. (From (1)) 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 14 years. He provides courses for Maths, Science and Computer Science at Teachoo