5. [AS3] To draw the perpendicular bisector, we use . (A) Ruler and divider (B) Ruler and compass (C) Ruler only (D)None of these Very Short Answer Type Questions 6. [AS2] Estimate whether a given line is perpendicular to the other line or not. (i) (ii) (iii) (iv) (v) EXERCISE 13.3. PERPENDICULARS 49
Long Answer Type Questions 7 [AS5] Constructing the perpendicular bisector of a given line segment. Draw a line segment of 15 cm and draw a perpendicular bisector of the given line segment. 8 [AS5] Draw a line segment AB of any length and find its mid point. 9 [AS4] Find the midpoint of CD which is at edge of a science text book. 10 [AS5] Using a ruler and compass, draw AB = 7.8 cm. Find its mid point. EXERCISE 13.3. PERPENDICULARS 50
EXERCISE 13.4 CONSTRUCTION OF ANGLES USING PROTRACTOR 13.4.1 Key Concepts Using a ruler and a compass, the following can be constructed: i. A circle, when the length of its radius is known e)120◦ ii. A line segment, if its length is given iii. A copy of a line segment iv. A perpendicular to a line through a point a. On the line b. Not on the line v. The perpendicular bisector of a line segment of a given length vi. An angle of a given measure vii. A copy of an angle viii. The bisector of a given angle ix. Some angles of special measures as: a)30◦ b)60◦ c)45◦ d)90◦ 13.4.2 Additional Questions Objective Questions 1. [AS3] The mathematical instrument which is used to construct angles is . (A) Ruler (B) Divider (C)Protractor (D)None of these 2. [AS3] An angle is measured in . (A) Degrees (B) Metres (C) Litres (D)Kilograms EXERCISE 13.4. CONSTRUCTION OF ANGLES USING PROTRACTOR 51
3. [AS3] The ray which divides the given angle into two equal measures is called . 52 (A) An angle bisector (B) A perpendicular bisector (C)A median (D)The centroid 4. [AS1] ∠AOB = 90◦ and OD is the bisector of ∠AOB. Then ∠AOD = . (A) 90◦ (B) 60◦ (C) 75◦ (D) 45◦ 5. [AS3] An angle whose measure is 90◦ is called . (A) An acute angle (B) An obtuse angle (C)A right angle (D)A reflex angle Short Answer Type Questions 6(i) [AS5] Construct ∠PQR = 85◦. Then construct the bisector of ∠PQR. (ii) [AS5] Construct ∠ABC = 90 ◦. Then construct the bisector of ∠ABC. Long Answer Type Questions 7 [AS5] Construct the following angles using a protractor: (i) ∠ABC = 35◦ (ii) ∠DEF = 40◦ (iii) ∠GHI = 110◦ (iv) ∠JKL = 145◦ (v) ∠MNO = 150◦ EXERCISE 13.4. CONSTRUCTION OF ANGLES USING PROTRACTOR
EXERCISE 13.5 CONSTRUCTING ANGLES OF SPECIAL MEASURES 13.5.1 Key Concepts i. Some special angles can be drawn without using a protractor. ii. We can bisect any angle using a compass. 13.5.2 Additional Questions Objective Questions 1. [AS3] Some angles of special measures such as 90◦, 45◦, 60◦, 30◦, 120◦ and 135◦ can be drawn using . (A) A ruler and divider (B) A ruler and a compass (C)Set squares (D)None of these 2. [AS3] An angle whose measure is 180◦ is called a/an . (A) Right angle (B) Straight angle (C)Acute angle (D)Obtuse angle 3. [AS3] An angle whose measure is 360◦ is called a . (A)Right angle (B) Straight angle (C)Complete angle (D)Reflex angle 4. [AS3] An angle whose measure is less than 90◦ and greater than zero degrees is called . (A) A right angle (B) An acute angle (C)An obtuse angle (D)A straight angle EXERCISE 13.5. CONSTRUCTING ANGLES OF SPECIAL MEASURES 53
5. [AS3] When two rays meet at a point, they form a / an . (A) Line segment (B) Angle (C) Line (D)None of these Short Answer Type Questions 6(i) [AS5] With the help of a compass and a ruler construct an angle of ∠ABC = 60◦. (ii) [AS5] With the help of a compass and a ruler, construct an angle of 120◦. 7(i) [AS5] Using a compass and a ruler, construct an angle of 45◦. (ii) [AS5] Using a compass and a ruler, construct the following angles: a) An angle of 75◦ b) An angle of 90◦ c) An angle of 150 ◦ 8(i) [AS5] Construct ∠PQR = 30◦ and draw another angle ∠ABC = ∠PQR using compass. (ii) [AS5] Construct ∠ABC = 60◦ and then draw another angle ∠XYZ = ∠ABC without using a protractor. EXERCISE 13.5. CONSTRUCTING ANGLES OF SPECIAL MEASURES 54
—— Project Based Questions —— (i) Mr. Raghavendra wants to distribute the prize money of Rs. 4,80,000 to all his four children in the following way. 1 th of the prize money to Ramya, 1 th of the prize money to Soumya, 2 th 8 6 5 3 th of the prize money to Kavya and 10 to Bhavya and the remaining for himself. Calculate the shares of each person and represent them pictorially with different colours. (ii) Go round your colony. Note how many houses of different kinds, i.e., thatched houses, tiled houses, RCC slab houses, duplex houses, apartments are there. Tabulate the findings and represent the data as a bar graph. (iii) Naveena and Praveena wish to make a pattern of F’s. They make one F using 4 match sticks as shown below. Continue the pattern and fill in the details in the table showing the number of F’s and the number of match sticks required as shown below. Number of F’s 12345678n Number of match sticks 4 8 (iv) The president of a colony in Hyderabad wants to build a path of width 5 metres around and inside a park of dimensions 155 metres by 105 metres. He wants to fence the path on all the sides with barbed wire for four rounds. Find the total amount he has to spend for the fencing if the cost of the barbed wire is Rs. 25 per metre. Draw a neat picture representing the above condition. (v) Take a square ruled paper and a dice. Throw the dice and note the number on it. Fill as many squares as the number noted with your favourite colour. Repeat the same for ten more times and colour the number of squares accordingly with different colours. a. Find the ratio of number of squares coloured with your favourite colour and the num- ber of squares with other colours. b. Find the ratio of the number of squares coloured first time with the total number of coloured squares. c. Find the ratio of number of squares coloured except the first time and the total num- ber of squares coloured. PROJECT BASED QUESTIONS 55
Additional AS Based Practice Questions Q1 [AS4] The marks (out of 10) obtained by 28 students in Mathematics test are listed as below: 8, 1, 2, 6, 5, 5, 5, 0, 1, 9, 7, 8, 0, 5, 8, 3, 0, 8, 10, 10, 3, 4, 8, 7, 8, 9, 2, 0 a) The number of students who obtained marks equal to or more than 5 is: A) 13 B) 15 C) 16 D) 17 b) The number of students who scored marks less than 4 is: A) 15 B) 13 C) 12 D) 10 Q2 [AS4] The choices of fruits of 42 students in a class are as follows: where A, B, G, M, O stand for the fruits Apple, Banana, Grapes, Mango and Orange respectively. a) Which two fruits are liked by an equal number of students? A) A and M B) M and B C) B and O D) B and G b) Which fruit is liked by most of the students? A) O B) G C) M D) A ADDITIONAL AS BASED PRACTICE QUESTIONS 56
State whether the statement is True or False and give reason for your answer. [AS2] Q3 To represent the population of different towns using bar graph, it is convenient to take one unit length to represent one person. Q4 In a bar graph, the gap between two consecutive bars may not be the same. Q5 [AS1] On the scale of 1 unit length = 10 crore, the bar of length 6 units will represent ________________ crore, and of ______________ units will represent 75 crore. Q6 [AS2] Which of the following equations has x = 2 as a solution? A) x + 2 = 5 B) x – 2 = 0 C) 2x + 1 = 0 D) x + 3 = 6 Q7 [AS5] The perimeter of the triangle shown in the given figure is: A) 2x + y B) x + 2y C) x + y D) 2x – y Q8 [AS2] Verify: 25 kg : 20 g = 50 kg : 40 g Q9 [AS2] Verify: The ratio of 150 cm to 1 m is 1 : 1.5. ADDITIONAL AS BASED PRACTICE QUESTIONS 57
10 [AS2] Draw an angle of 80º using a protractor and divide it into four equal parts, using a ruler and a compass. Check and verify your construction by measurement. Q11 [AS2] Draw a circle of 6 cm radius using a ruler and a compass. Draw one of its diameters and then the perpendicular bisector of this diameter. Check and verify if this perpendicular bisector contains another diameter of the circle. ADDITIONAL AS BASED PRACTICE QUESTIONS 58
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