Practical Geometry MCQs with answers

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Q. In ΔRST, R = 5 cm, and ∠SRT = 45° and ∠RST = 45°. Which criterion can be used to construct ΔRST?
  • (A) A.S.A. criterion
  • (B) S.A.S. criterion
  • (C) S.S.S. criterion
  • (D) R.H.S. criterion
💬 Discuss
✅ Correct Answer: (A) A.S.A. criterion
Q. Identify the criterion of construction of the equilateral triangle LMN given LM = 6 cm.
  • (A) S.A.S. criterion
  • (B) R.H.S. criterion
  • (C) A.S.A. criterion
  • (D) S.S.S. criterion
💬 Discuss
✅ Correct Answer: (D) S.S.S. criterion
Q. The idea of equal alternate angles is used to construct which of the following?
  • (A) A line parallel to a given line
  • (B) A triangle
  • (C) A square
  • (D) Two triangles
💬 Discuss
✅ Correct Answer: (A) A line parallel to a given line
Q. A Given AB = 3 cm, AC = 5 cm,and ∠B = 30°, ΔABC cannot be uniquely constructed, with AC as base, why?
  • (A) Two sides and included angle are given.
  • (B) The other two angles are not given.
  • (C) The vertex B cannot be uniquely located.
  • (D) The vertex A coincides with the vertex C.
💬 Discuss
✅ Correct Answer: (C) The vertex B cannot be uniquely located.
Q. A line panda point X not on it are given. Which of the following is used to draw a line parallel to p through X?
  • (A) Equal corresponding angles.
  • (B) Congruent triangles.
  • (C) Angle sum property of triangles.
  • (D) Pythagoras’ theorem.
💬 Discuss
✅ Correct Answer: (A) Equal corresponding angles.
Q. Δ PQR is such that ∠P = ∠Q = ∠R = 60° which of the following is true?
  • (A) Δ PQR is equilateral.
  • (B) Δ PQR is acute angled.
  • (C) Both A and B
  • (D) none of these
💬 Discuss
✅ Correct Answer: (C) Both A and B
Q. Which vertex of ΔABC is right angled if AB_________ = 8 cm, AC________ = 6 cm,and BC________ = 10 cm,?
  • (A) ∠C
  • (B) ∠A
  • (C) ∠B
  • (D) A or C
💬 Discuss
✅ Correct Answer: (B) ∠A
Q. An isosceles triangle is constructed as shown in the figure.
Which of the given statements is incorrect?
  • (A) PR______ is the hypotenuse of ΔPQR.
  • (B) ΔPQR is an equilateral triangle.
  • (C) ΔPQR is a right angled triangle.
  • (D) If right angled ΔPQR has its equal angles measuring 45° each.
💬 Discuss
✅ Correct Answer: (B) ΔPQR is an equilateral triangle.
Q. ΔPQR is constructed with all its angles measuring 60° each. Which of the following is correct?
  • (A) ΔPQR is an equilateral triangle.
  • (B) ΔPQR is isosceles triangle.
  • (C) ΔPQR is a scalene triangle.
  • (D) ΔPQR is a right angled triangle.
💬 Discuss
✅ Correct Answer: (A) ΔPQR is an equilateral triangle.
Q. How many perpendicular lines can be drawn to a line from a point not on it?
  • (A) 0
  • (B) 1
  • (C) 2
  • (D) Infinite
💬 Discuss
✅ Correct Answer: (B) 1
Q. Identify the false statement.
  • (A) A triangle with three equal sides is called an equilateral triangle.
  • (B) A triangle with a right angle is called a right angled triangle.
  • (C) A triangle with two equal sides is called a scalene triangle
  • (D) A right angled triangle has two acute angles and a right angle.
💬 Discuss
✅ Correct Answer: (C) A triangle with two equal sides is called a scalene triangle
Q. ΔPQR is constructed such that PQ = 5 cm, PR = 5 cm and ∠RPQ = 50° Identify the type of triangle constructed.
  • (A) An isosceles triangle
  • (B) An acute angled triangle
  • (C) An obtuse angled triangle
  • (D) Both A and B
💬 Discuss
✅ Correct Answer: (D) Both A and B
Q. Which of the following is NOT constructed using a ruler and a set square?
  • (A) A perpendicular to a line from a point not on it.
  • (B) A perpendicular bisector of a line segment.
  • (C) A perpendicular to a line at a point on the line.
  • (D) A line parallel to a given line through a given point.
💬 Discuss
✅ Correct Answer: (B) A perpendicular bisector of a line segment.
Q. Study the steps of construction given.
Step 1: Draw a ray OA.
Step 2: With O as centre and any convenient radius draw an arc MN to cut OA at M.
Step 3: With M as centre and the same radius draw an arc to cut MN at P.
Step 4: With P as centre and the same radius, draw an arc to cut MN at Q.
Step 5: Draw OQ and produce it to D. An angle AOD is constructed.
What is the measure of ∠AOD?
  • (A) 60°
  • (B) 30°
  • (C) 120°
  • (D) 45°
💬 Discuss
✅ Correct Answer: (C) 120°
Q. In ΔXYZ, x, y and z denote the three sides. Which of the following is incorrect’?
  • (A) x – y > z
  • (B) x + z > y
  • (C) x – y < z
  • (D) x + y > z
💬 Discuss
✅ Correct Answer: (A) x – y > z
Q. In which of the following cases can a triangle be constructed?
  • (A) Measures of three sides are given.
  • (B) Measures of two sides and an included angle are given.
  • (C) Measures of two angles and the side between them are given.
  • (D) All the above.
💬 Discuss
✅ Correct Answer: (D) All the above.
Q. Based on the sides of a triangle, which of the following is a classification of triangles?
  • (A) A right angled triangle
  • (B) An acute angled triangle
  • (C) An obtuse angled triangle
  • (D) An isosceles triangle
💬 Discuss
✅ Correct Answer: (D) An isosceles triangle
Q. Which of the following is used to draw a line parallel to a given line?
  • (A) A protractor
  • (B) A set square
  • (C) A ruler
  • (D) A ruler and compasses
💬 Discuss
✅ Correct Answer: (D) A ruler and compasses
Q. A Choose the correct option in which a triangle CANNOT be constructed with the given lengths of sides.
  • (A) 3 cm, 4 cm, 5 cm
  • (B) 7 cm, 6 cm, 5 cm
  • (C) 10 cm, 7 cm, 2 cm
  • (D) 12 cm, 8 cm, 6 cm
💬 Discuss
✅ Correct Answer: (C) 10 cm, 7 cm, 2 cm
Q. Identify the true statement.
  • (A) A triangle with 3 equal sides is isosceles.
  • (B) A triangle with a 110° angle is right angled.
  • (C) A triangle with 3 acute angles is acute angled.
  • (D) A triangle with 2 equal sides is equilateral.
💬 Discuss
✅ Correct Answer: (C) A triangle with 3 acute angles is acute angled.
Q. Which of the following statements is incorrect?
  • (A) The sum of angles in a triangle is 2 right angles.
  • (B) The exterior angle of a triangle is equal to the interior angle of the triangle.
  • (C) The hypotenuse is the longest side of a right angled triangle.
  • (D) All the above.
💬 Discuss
✅ Correct Answer: (B) The exterior angle of a triangle is equal to the interior angle of the triangle.
Q. A triangular sign board is isosceles. If the unequal side is 7 cm and one of the equal sides is 6 cm, what is the measure of the third side?
  • (A) 5 cm
  • (B) 6 cm
  • (C) 7 cm
  • (D) Either A or C
💬 Discuss
✅ Correct Answer: (B) 6 cm
Q. In the given figure, find the measure of ∠ROT, if PQ = QR and ∠QPR = 60°.
  • (A) 60°
  • (B) 140°
  • (C) 120°
  • (D) 100°
💬 Discuss
✅ Correct Answer: (C) 120°
Q. Which among the following is used to construct a triangle?
  • (A) The lengths of the three sides.
  • (B) The perimeter of the triangle.
  • (C) The measures of three angles.
  • (D) The names of three vertices.
💬 Discuss
✅ Correct Answer: (A) The lengths of the three sides.

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Table of contents

  1. In ΔRST, R = 5 cm, and ∠SRT = 45° and ∠RST = 45°. Which criterion can be used to construct
  2. Identify the criterion of construction of the equilateral triangle LMN given LM = 6 cm.
  3. The idea of equal alternate angles is used to construct which of the following?
  4. A Given AB = 3 cm, AC = 5 cm,and ∠B = 30°, ΔABC cannot be uniquely constructed, with AC as base
  5. A line panda point X not on it are given. Which of the following is used to draw a line parallel to
  6. Δ PQR is such that ∠P = ∠Q = ∠R = 60° which of the following is true?
  7. Which vertex of ΔABC is right angled if AB_________ = 8 cm, AC________ = 6 cm,and BC________ = 10
  8. An isosceles triangle is constructed as shown in the figure. Which of the given statements is inco
  9. ΔPQR is constructed with all its angles measuring 60° each. Which of the following is cor
  10. How many perpendicular lines can be drawn to a line from a point not on it?
  11. Identify the false statement.
  12. ΔPQR is constructed such that PQ = 5 cm, PR = 5 cm and ∠RPQ = 50° Identify the type of triangle
  13. Which of the following is NOT constructed using a ruler and a set square?
  14. Study the steps of construction given. Step 1: Draw a ray OA. Step 2: With O as centre and any con
  15. In ΔXYZ, x, y and z denote the three sides. Which of the following is incorrect’?
  16. In which of the following cases can a triangle be constructed?
  17. Based on the sides of a triangle, which of the following is a classification of triangles?
  18. Which of the following is used to draw a line parallel to a given line?
  19. A Choose the correct option in which a triangle CANNOT be constructed with the given lengths of sid
  20. Identify the true statement.
  21. Which of the following statements is incorrect?
  22. A triangular sign board is isosceles. If the unequal side is 7 cm and one of the equal sides is 6 c
  23. In the given figure, find the measure of ∠ROT, if PQ = QR and ∠QPR = 60°.
  24. Which among the following is used to construct a triangle?