MCQ Questions For Class 6 Maths Chapter 14 Practical ... - Learn Insta

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Practical Geometry Class 6 MCQs Questions with Answers

Question 1. A line segment \(\overrightarrow { TP } \) is bisected at I. What is the measure of \(\overrightarrow { TI }\)? (a) \(\frac{1}{2}\)\(\overrightarrow { TP }\) (b) \(\overrightarrow { IP }\) (c) \(\overrightarrow { TP }\) (d) \(\frac{1}{3}\) \(\overrightarrow { TP }\)

Answer

Answer: (b) \(\overrightarrow { IP }\) Hint: \(\overrightarrow { TI }\) = \(\frac{1}{3}\) \(\overrightarrow { TP }\) = IP

Question 2. Which of the following can be drawn on a piece of paper? (a) A line (b) A line segment (c) A ray (d) A plane

Answer

Answer: (b) A line segment

Question 3. l || m. P and Q are points on land m respectively such that PQ ⊥ lR is a point on a line n in the same plane such that \(\overline { PQ }\) = \(\overline { QR }\). Which of the following is true? (a) l || n (b) m || n (c) Both [a] and [b] (d) Neither [a] nor [b]

Answer

Answer: (c) Both [a] and [b] Hint: Clearly, from the given data and the figure, l || n and m || n.

Question 4. At 7 a.m. the angle between the Sun’s ray and the ground at a point is 43°. What would be the angle at 10 a.m.? (a) 40° (b) 90° (c) Between 43° and 90° (d) Greater than 90°

Answer

Answer: (c) Between 43° and 90° Hint: Let QP be the sun’s ray and RP be the ground. The angle between QP and PR at P is 43° at 7 a.m. At 10 a.m., the sun’s ray is Q’P. We know that at 12 noon the sun is exactly above our head. So, the sun’s ray will be perpendicular to the ground. So, clearly at 10 am, the required angle will be between 43° and 90°.

Question 5. \(\overrightarrow { XY }\) divides ∠MXN = 72° in the ratio 1 : 2. What is the measure of ∠YXN? (a) 48° (b) 24° (c) 72° (d) 96°

Answer

Answer: (a) 48° Hint: Given ∠MXN = 72∘ and \(\overrightarrow { XY }\) divides ∠MXN in the ratio 1 : 2. ∠YXN = \(\frac{2}{3}\) ∠MXN = \(\frac{2}{3}\) × 72° = 48°

Question 6. \(\overrightarrow { MN }\) is the perpendicular bisector of \(\overleftrightarrow { AB }\). Which of the given statements is correct? (i) ∠ANM + ∠MNB = 90∘ (ii) \(\overline { AN }\) = \(\overline { NB }\) (iii) \(\overline { AN }\) = 2 \(\overline { NB }\) (iv) ∠MNB = \(\frac{1}{2}\) ∠ANM (a) (i) and (iii) only (b) (ii) and (iv) only (c) (i) and (ii) only (d) (ii) and (iii) only

Answer

Answer: (c) (i) and (ii) only Hint: \(\overrightarrow { NM }\) ⊥ \(\overleftrightarrow { AB }\) and \(\overrightarrow { NM }\) divides \(\overleftrightarrow { AB }\) into two congruent parts. Clearly ∠ANM = ∠MNB = 90∘ is true. \(\overline { AN }\) = \(\overline { NB }\) is true since \(\overrightarrow { NM }\) ⊥ \(\overleftrightarrow { AB }\), \(\overline { AN }\) = 2\(\overline { NB }\) is false, and ∠MNB = \(\frac{1}{2}\) ∠ANM is false. Thus, only (i) and (ii) are correct.

Question 7 Identify the uses of a ruler. (a) To draw a line segment of a given length (b) To draw a copy of a given segment. (c) To draw a diameter of a circle. (d) All the above.

Answer

Answer: (d) All the above. Hint: A ruler is used to draw a line segment of a given length, to draw the copy of a given segment, and to draw a diameter of a circle. Thus, all the given options are correct.

Question 8. P is the midpoint of \(\overline { AB }\). M and N are midpoints of \(\overline { AP }\) respectively. What is the measure of \(\overline { MN }\)? (a) \(\frac{1}{3}\) \(\overline { AB }\) (b) \(\frac{1}{2}\) \(\overline { AB }\) (c) \(\frac{1}{2}\) \(\overline { AP }\) (d) \(\frac{3}{2}\) \(\overline { AB }\)

Answer

Answer: (b) \(\frac{1}{2}\) \(\overline { AB }\) Hint: P is the midpoint of \(\overline { AB }\) ⇒ AP = PB M and N are midpoints of \(\overline { AP }\) and \(\overline { PB }\) ⇒ \(\overline { AM }\) = \(\overline { MP }\) and \(\overline { PN }\) = \(\overline { NB }\) ∴ \(\overline { MN }\) = \(\overline { MP }\) + \(\overline { PN }\) = \(\frac{1}{2}\) \(\overline { AP }\) + \(\frac{1}{2}\) \(\overline { PB }\) = \(\frac{1}{2}\) (\(\overline { AP }\) + \(\overline { PB }\) ) = \(\frac{1}{2}\) (\(\overline { AB }\))

Question 9. \(\overrightarrow { XY }\) bisects∠AXB. If ∠YXB = 37.5∘, what is the measure of ∠AXB? (a) 37.5° (b) 74° (c) 64° (d) 75°

Answer

Answer: (d) 75°

Question 10. X and Y are two distinct points in a plane. How many lines can be drawn passing through both X and Y? (a) 0 (b) 1 (c) Only 2 (d) Infinitely many

Answer

Answer: (b) 1

Question 11. Lines a, b, p, q, m, n and x have a point P common to all of them. What is the name of P? (a) Point of concurrence (b) Point of intersection (c) Common point (d) Distinct point

Answer

Answer: (a) Point of concurrence Hint: A point common to multiple lines is called a point of concurrence as the lines are concurrent lines.

Question 12. \(\overrightarrow { QZ }\) is the bisector of ∠PQZ = ∠PQR. Which of the following is true? (a) ∠PQZ = ∠PQR (b) ∠PQZ = ∠ZQR (c) ∠PQZ = \(\frac{1}{2}\) ∠ZQR (d) Both [b] and [c]

Answer

Answer: (d) Both [b] and [c] Hint: \(\overrightarrow { QZ }\) bisects ∠PQR (Given) Thus. ∠PQZ = ∠ZQR = \(\frac{1}{2}\) ∠PQR

Question 13. Identify the pair of parallel lines. (i) Lines m and n have two points in common. (ii) Lines p and q do not have any point in common (iii) Lines p and q have a point X in common. (a) (i) and (ii) only (b) (ii) only (c) (ii) and (iii) only (d) (i), (ii) and (iii)

Answer

Answer: (b) (ii) only Hint: Parallel lines do not have any point in common.

Question 14. Identify the one with no definite length. (a) \(\overleftrightarrow { AB }\) (b) \(\overline { PQ }\) (c) -XYZ (d) \(\overline { MN }\)

Answer

Answer: (a) \(\overleftrightarrow { AB }\) Hint: \(\overleftrightarrow { AB }\) has no definite length.

Question 15. If two lines have only one point in common, what are they called? (a) Parallel lines (b) Intersecting lines (c) Perpendicular lines (d) Transversal

Answer

Answer: (b) Intersecting lines Hint: Intersecting lines have only one point in common.

Question 16. Two lines are said to be perpendicular to each other when they meet at ____angle. (a) 180° (b) 90° (c) 60° (d) 360°

Answer

Answer: (b) 90°

Question 17. A line segment \(\overline { IP }\) is bisected at T. Which of the following equals \(\overline { IT }\)? (a) \(\overline { IP }\) (b) \(\overline { TP }\) (c) \(\overline { TC }\) (d) \(\overline { IQ }\)

Answer

Answer: (b) \(\overline { TP }\)

Question 18. How do you draw a 90° angle? (a) By drawing a perpendicular to a line from a point lying on it. (b) By bisecting a 120° angle. (c) By bisecting a 60° angle. (d) By drawing multiples of 45° angle.

Answer

Answer: (a) By drawing a perpendicular to a line from a point lying on it.

Question 19. An angle of 15° is drawn using a pair of compasses and a ruler. How is it done? (a) Bisecting 60° angle. (b) Bisecting 60° and 120° angles. (c) Bisecting 60° and then bisecting it again. (d) Bisecting a 60° and 180° angles.

Answer

Answer: (c) Bisecting 60° and then bisecting it again.

Question 20. Identify the instruments used to bisect a given line segment. (a) A scale and a protractor (b) Scale and compasses (c) Scale and setsquares (d) A scale

Answer

Answer: (b) Scale and compasses

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