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Lines and Angles — Maths STD 9 — Question

Gujarat BoardEnglish MediumSTD 9MathsLines and Angles4 Marks
Question
The figure below shows an equilateral triangle bounded by two straight lines. 

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5. What is the sum of the four marked angles?
  A. 180°
  B. 240°
  C. 270°
  D. 360°

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Answer

5. B. 240

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Mr. Roy, a Mathematics teacher explained some key points of unit 1 of class IX to his students. Some are given here.
• There are infinite rational numbers between any two rational numbers.
• Rationalisation of a denominator means to change the irrational denominator to rational form.
• A number is irrational if its decimal form is non-terminating and non-recurring. On the basis of these key points, choose the correct option in the following questions:
(i) What is the reciprocal of $2+\sqrt{3}$ ?
(a) $\sqrt{3}+2$ $\quad$(b) $\frac{1}{\sqrt{3}-2}$$\quad$ (c) $2-\sqrt{3}$ $\quad$(d) $\frac{1}{2}+\frac{1}{\sqrt{3}}$
(ii) Which of the following is irrational?
(a) $\frac{\sqrt{4}}{\sqrt{9}}$$\quad$ (b) $\frac{\sqrt{12}}{\sqrt{3}}$ $\quad$(c) $\sqrt{7}$ $\quad$(d) $\sqrt{81}$
(iii) Which of the following is irrational?
(a) 0.14 $\quad$(b) $0.14 \overline{16}$ $\quad$(c) $0.1 \overline{416}$ $\quad$(d) 0.401400140001......
(iv) Which of the following is value of $(\sqrt{11}+\sqrt{7})(\sqrt{11}-\sqrt{7})$ ?
(a) $\sqrt{11}$$\quad$ (b) 4 $\quad$(c) -4 $\quad$(d) $\sqrt{7}$
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Four persons John, Saurabh, Salim and Ratan are sitting in a courtyard at points A, B, C and D respectively as shown in Fig. The courtyard has been divided into small squares by drawing equally spaced horizontal and vertical lines. Taking OX and OY as the coordinates axes answer the following questions:
Image
(i) The distance between John and Salim is
(a) 6 units $\quad$(b) 4 units $\quad$(c) 5 units $\quad$(d) 7 units
(ii) The distance between John and Saurabh is
(a) 6 units $\quad$(b) $3 \sqrt{2}$ units $\quad$(c) $6 \sqrt{2}$ units $\quad$(d) $2 \sqrt{2}$ units
(iii) The distance between John and Ratan is
(a) $2 \sqrt{5}$ units $\quad$(b) $2 \sqrt{10}$ units $\quad$(c) $\sqrt{5}$ units $\quad$(d) 20 units
(i) The coordinates of point A are
(a) $(4,3)$ $\quad$(b) $(3,4)$ $\quad$(c) $(3,3)$ $\quad$(d) $(4,4)$
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'Learning by doing' has great impact in teaching of Maths. Students also enjoy Mathematics by activity method. Mr. Paul, a Mathematics teacher has explained the topic of Lines and Angles by taking a very thin steel wire. He used steel wire and made some shapes at some specific angles and shown to students and asked questions.
Image
Choose the correct option in the following questions:
(i) What is the measure of $\angle B O D$ in figure?
(a) $90^{\circ}$$\quad$(b) $70^{\circ}$$\quad$(c) $80^{\circ}$$\quad$(d) $100^{\circ}$
(ii) What is measure of $\angle y$ in figure ?
(a) $110^{\circ}$$\quad$(b) $90^{\circ}$$\quad$(c) $140^{\circ}$$\quad$(d) $100^{\circ}$$\quad$
(iii) What is the measure of $\angle a$ and $\angle b$ respectively in Figure, if a : b = 2 : 3 and $O P \perp X Y$ ?
(a) $54^{\circ}, 36^{\circ}$$\quad$(b) $36^{\circ}, 54^{\circ}$$\quad$(c) $60^{\circ}, 90^{\circ}$$\quad$(d) $40^{\circ}, 60^{\circ}$
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(a) $144^{\circ}$$\quad$(b) $90^{\circ}$$\quad$(c) $126^{\circ}$$\quad$(d) $120^{\circ}$
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2. A carton contains both fragrant and non-fragrant liquid soap bottles.
Write an equation representing the number of fragrant and non-fragrant bottles in the carton.
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This is the picture of a gas balloon illed with helium gas.

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This balloon has 18 faces that are square in shape and 8 equilateral faces that are triangular.
3. Which of the following is the net of the balloon?

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4. The side length of the square is 20 cm. What is the total surface area of the balloon?

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In the quadrilateral ABCD given below, ∠DAC = 90° and AB = AC = AD = DE = EB.

Image
8. What is the value of ∠EAC?
  A. 15°
  B. 30°
  C. 45°
  D. 90°
9. Which type of quadrilateral is ABCE?
   A. Rhombus
   B. Kite
  C. Trapezium
  D. Parallelogram
10. What is the value of ∠ABE?
  A. 20°
  B. 30°
  C. 45°
  D. 60°

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Draws a graphical representation of the points scored by team B.
His graphical representation is given below.

Image
10. Suman says, “Arun’s graphical representation is not appropriate.” 
Do you agree with Suman? Mention YES or NO. Give reason to justify your choice.

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Read the Source/ Text given below and answer any four questions:

Chocolate is in the form of a quadrilateral with sides 6cm and 10cm, 5cm and 5cm(as shown in the figure) is cut into two parts on one of its diagonal by a lady. Part-I is given to her maid and part II is equally divided among a driver and gardener.
  1. Length of BD:
  1. 9cm
  2. 8cm
  3. 7cm
  4. 6cm
  1. Area of $\triangle\text{ABC}:$
  1. 24cm2
  2. 12cm2
  3. 42cm2
  4. 21cm2
  1. The sum of all the angles of a quadrilateral is equal to:
  1. 180°
  2. 270°
  3. 360°
  4. 90°
  1. A diagonal of a parallelogram divides it into two congruent:
  1. Square.
  2. Parallelogram.
  3. Triangles.
  4. Rectangle.
  1. Each angle of the rectangle is:
  1. More than 90°
  2. Less than 90°
  3. Equal to 90°
  4. Equal to 45°
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Read the Source/ Text given below and answer these questions:

In the above picture, one small square is of size 1km × 1km. From the starting point O(0, 0) Deepak started to drive towards his home. He first drives 3km in left then he turned to his left and drove 2km, there he found a temple. He worshipped there and drove 6km in the left direction, there is a zoo and from the zoo, he drives 2km on the right side, then he reached his home. From O Sanjay drove for his school, he drove 1km to his right then took a left turn and drives 2km then again took a right turn and drives 2km. He found a hospital in the way. From Hospital he drove 3km and finally reached his school.
  1. What are the coordinates of the Hospital?
  1. (3, 2)
  2. (2, 3)
  3. (3, 3)
  4. (5, 5)
  1. What is common abscissa of school, Hospital, Zoo and Deepak's home?
  1. 3
  2. 5
  3. -3
  4. -5
  1. What is the common ordinate of temple and Zoo?
  1. 3
  2. 5
  3. -3
  4. -2
  1. Deepak Drove in which quadrants?
  1. I & II
  2. II and III
  3. III and IV
  4. IV and I
  1. Sanjay Drove in which quadrants?
  1. I only
  2. II and III
  3. III and IV
  4. II and I
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A zoo is in the shape of an isosceles trapezium.
It is divided into three zones – Zone 1, Zone 2 and Zone 3.
Animals are kept without cages in Zone 1. Zone 2 is for visitors and Zone 3 is reserved for park
authorities. 

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To avoid the entry of animals in zones 2 and 3, a 1.8 km long wired fencing is installed.
7. Which of the following calculations shows the area for animals?
  A. √1.35×0.65×1.15
  B. 2.15×0.35×0.65×1.15
  C. √3.15×1.35×1.65×1.15
  D. √4.30×1.35×0.65×1.15
8. “The area reserved for animals is twice the area reserved for the zoo authorities.” Do you have enough information to support this statement? Explain your answer.

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