Seema placed a light bulb at point O on the  ceiling and directly below it placed a table. Now,  she put a cardboard of shape ABCD between  table and lighted bulb. Then a shadow of ABCD  is casted on the table as A'B'C'D' (see figure).  Quadrilateral A'B'C'D' in an enlargement of ABCD  with scale factor 1: 2, Also, AB = 1.5 cm, BC = 25  cm, CD = 2.4 cm and AD = 2.1 cm; ∠A = 105°, ∠B  = 100°, ∠C = 70° and ∠D = 85°.

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Question 1

What is the measurement of angle A’?

(a) 105°  

(b) 100°

(c) 70° 

(d) 80°
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Question 2

What is the length of A'B’?

(a) 1.5 cm  

(b) 3 cm

(c) 5 cm 

(d) 2.5 cm

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Question 3

What is the sum of angles of quadrilateral A'B'C'D’?

(a) 180°  

(b) 360°

(c) 270° 

(d) None of these

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Question 4

What is the ratio of sides A'B' and A'D’?

(a) 5: 7  

(b) 7: 5

(c) 1: 1  

(d) 1: 2

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Question 5

What is the sum of angles C' and D’?

(a) 105°  

(b) 100°

(c) 155°  

(d) 140°

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Transcript

Question Seema placed a light bulb at point O on the ceiling and directly below it placed a table. Now, she put a cardboard of shape ABCD between table and lighted bulb. Then a shadow of ABCD is casted on the table as A'B'C'D' (see figure). Quadrilateral A'B'C'D' in an enlargement of ABCD with scale factor 1: 2, Also, AB = 1.5 cm, BC = 25 cm, CD = 2.4 cm and AD = 2.1 cm; ∠A = 105°, ∠B = 100°, ∠C = 70° and ∠D = 85°. Since the two quadrilaterals are similar Angles will be the same Sides have the ratio as that of scale factor, i.e. 1 : 2 Therefore, ∠A’ = 105°, ∠B’ = 100°, ∠C’ = 70° and ∠D’ = 85° For sides: 𝑨𝑩/(𝑨^′ 𝑩^′ )=𝑩𝑪/(𝑩^′ 𝑪^′ )=𝑪𝑫/(𝑪^′ 𝑫^′ )=𝑨𝑫/(𝑨^′ 𝑫^′ )=𝟏/𝟐 A’B’ = 2 × AB = 2 × 1.5 = 3 cm B’C’ = 2 × BC = 2 × 2.5 = 5 cm C’D’ = 2 × CD = 2 × 2.4 = 4.8 cm A’D’ = 2 × AD = 2 × 2.1 = 4.2 cm Question 1 What is the measurement of angle A’? (a) 105° (b) 100° (c) 70° (d) 80° Here, ∠A' = ∠A ∠ A' = 105° So, the correct answer is (A) Question 2 What is the length of A'B’? (a) 1.5 cm (b) 3 cm (c) 5 cm (d) 2.5 cm Now, A’B’ = 2 × AB = 2 × 1.5 = 3 cm So, the correct answer is (B) Question 3 What is the sum of angles of quadrilateral A'B'C'D’? (a) 180° (b) 360° (c) 270° (d) None of these We know that Sum of angles of any quadrilateral = 360° Sum of angles of A'B'C'D' = 360° So, the correct answer is (B) Question 4 What is the ratio of sides A'B' and A'D’? (a) 5: 7 (b) 7: 5 (c) 1: 1 (d) 1: 2 We found that, A’B’ = 3 cm A’D’ = 4.2 cm Now, ∴ (𝑨^′ 𝑩)/(𝑨^′ 𝑫) = 3/4.2 = 30/42 = 5/7 or 5 : 7 So, the correct answer is (A) Question 5 What is the sum of angles C' and D’? (a) 105° (b) 100° (c) 155° (d) 140° Now, ∴ ∠C' + ∠ D' = 70° + 85° = 155° So, the correct answer is (C)

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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 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.