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Geometry MCQ & Objective Questions

Geometry is a crucial subject in mathematics that plays a significant role in various school and competitive exams. Mastering this topic not only enhances your spatial understanding but also boosts your problem-solving skills. Practicing Geometry MCQs and objective questions is essential for scoring better in exams, as it helps you familiarize yourself with important concepts and question patterns. With the right practice questions, you can identify key areas to focus on during your exam preparation.

What You Will Practise Here

Basic geometric shapes and their properties
Angles, lines, and their relationships
Triangles: types, congruence, and similarity
Quadrilaterals and their characteristics
Circles: radius, diameter, chords, and tangents
Area and perimeter calculations for various shapes
Volume and surface area of 3D figures

Exam Relevance

Geometry is a fundamental part of the mathematics syllabus for CBSE, State Boards, and competitive exams like NEET and JEE. In these exams, you can expect questions that test your understanding of geometric properties, theorems, and problem-solving abilities. Common question patterns include multiple-choice questions that require you to apply formulas and concepts to solve real-world problems. Being well-prepared in Geometry can significantly enhance your performance in these assessments.

Common Mistakes Students Make

Misunderstanding the properties of different geometric shapes
Confusing theorems related to triangles and quadrilaterals
Errors in calculating area and volume due to incorrect formula application
Overlooking the importance of diagrams in problem-solving

FAQs

Question: What are some important Geometry MCQ questions I should focus on?
Answer: Focus on questions related to the properties of shapes, theorems, and area and volume calculations, as these are frequently tested in exams.

Question: How can I improve my Geometry problem-solving skills?
Answer: Regular practice of Geometry objective questions with answers will help you understand concepts better and improve your speed and accuracy.

Start solving Geometry practice MCQs today to test your understanding and boost your confidence for upcoming exams. Remember, consistent practice is the key to mastering Geometry!

Angles and Parallel Lines Angles and Parallel Lines - Applications Angles and Parallel Lines - Case Studies Angles and Parallel Lines - Coordinate Geometry Applications Angles and Parallel Lines - Coordinate Geometry Applications - Applications Angles and Parallel Lines - Coordinate Geometry Applications - Case Studies Angles and Parallel Lines - Coordinate Geometry Applications - Problem Set Angles and Parallel Lines - Problem Set Angles and Parallel Lines - Problems on Circles Angles and Parallel Lines - Problems on Circles - Applications Angles and Parallel Lines - Problems on Circles - Case Studies Angles and Parallel Lines - Problems on Circles - Problem Set Angles and Parallel Lines - Problems on Triangles Angles and Parallel Lines - Problems on Triangles - Applications Angles and Parallel Lines - Problems on Triangles - Case Studies Angles and Parallel Lines - Problems on Triangles - Problem Set Angles and Parallel Lines - Proof-based Questions Angles and Parallel Lines - Proof-based Questions - Applications Angles and Parallel Lines - Proof-based Questions - Case Studies Angles and Parallel Lines - Proof-based Questions - Problem Set Basic Geometric Concepts Basic Geometric Concepts - Applications Basic Geometric Concepts - Case Studies Basic Geometric Concepts - Coordinate Geometry Applications Basic Geometric Concepts - Coordinate Geometry Applications - Applications Basic Geometric Concepts - Coordinate Geometry Applications - Case Studies Basic Geometric Concepts - Coordinate Geometry Applications - Problem Set Basic Geometric Concepts - Problem Set Basic Geometric Concepts - Problems on Circles Basic Geometric Concepts - Problems on Circles - Applications Basic Geometric Concepts - Problems on Circles - Case Studies Basic Geometric Concepts - Problems on Circles - Problem Set Basic Geometric Concepts - Problems on Triangles Basic Geometric Concepts - Problems on Triangles - Applications Basic Geometric Concepts - Problems on Triangles - Case Studies Basic Geometric Concepts - Problems on Triangles - Problem Set Basic Geometric Concepts - Proof-based Questions Basic Geometric Concepts - Proof-based Questions - Applications Basic Geometric Concepts - Proof-based Questions - Case Studies Basic Geometric Concepts - Proof-based Questions - Problem Set Circles - Theorems and Properties Circles - Theorems and Properties - Applications Circles - Theorems and Properties - Case Studies Circles - Theorems and Properties - Coordinate Geometry Applications Circles - Theorems and Properties - Coordinate Geometry Applications - Applications Circles - Theorems and Properties - Coordinate Geometry Applications - Case Studies Circles - Theorems and Properties - Coordinate Geometry Applications - Problem Set Circles - Theorems and Properties - Problem Set Circles - Theorems and Properties - Problems on Circles Circles - Theorems and Properties - Problems on Circles - Applications Circles - Theorems and Properties - Problems on Circles - Case Studies Circles - Theorems and Properties - Problems on Circles - Problem Set Circles - Theorems and Properties - Problems on Triangles Circles - Theorems and Properties - Problems on Triangles - Applications Circles - Theorems and Properties - Problems on Triangles - Case Studies Circles - Theorems and Properties - Problems on Triangles - Problem Set Circles - Theorems and Properties - Proof-based Questions Circles - Theorems and Properties - Proof-based Questions - Applications Circles - Theorems and Properties - Proof-based Questions - Case Studies Circles - Theorems and Properties - Proof-based Questions - Problem Set Coordinate Geometry - Distance and Section Formula Coordinate Geometry - Distance and Section Formula - Applications Coordinate Geometry - Distance and Section Formula - Case Studies Coordinate Geometry - Distance and Section Formula - Coordinate Geometry Applications Coordinate Geometry - Distance and Section Formula - Coordinate Geometry Applications - Applications Coordinate Geometry - Distance and Section Formula - Coordinate Geometry Applications - Case Studies Coordinate Geometry - Distance and Section Formula - Coordinate Geometry Applications - Problem Set Coordinate Geometry - Distance and Section Formula - Problem Set Coordinate Geometry - Distance and Section Formula - Problems on Circles Coordinate Geometry - Distance and Section Formula - Problems on Circles - Applications Coordinate Geometry - Distance and Section Formula - Problems on Circles - Case Studies Coordinate Geometry - Distance and Section Formula - Problems on Circles - Problem Set Coordinate Geometry - Distance and Section Formula - Problems on Triangles Coordinate Geometry - Distance and Section Formula - Problems on Triangles - Applications Coordinate Geometry - Distance and Section Formula - Problems on Triangles - Case Studies Coordinate Geometry - Distance and Section Formula - Problems on Triangles - Problem Set Coordinate Geometry - Distance and Section Formula - Proof-based Questions Coordinate Geometry - Distance and Section Formula - Proof-based Questions - Applications Coordinate Geometry - Distance and Section Formula - Proof-based Questions - Case Studies Coordinate Geometry - Distance and Section Formula - Proof-based Questions - Problem Set Mensuration of 2D Shapes Mensuration of 2D Shapes - Applications Mensuration of 2D Shapes - Case Studies Mensuration of 2D Shapes - Coordinate Geometry Applications Mensuration of 2D Shapes - Coordinate Geometry Applications - Applications Mensuration of 2D Shapes - Coordinate Geometry Applications - Case Studies Mensuration of 2D Shapes - Coordinate Geometry Applications - Problem Set Mensuration of 2D Shapes - Problem Set Mensuration of 2D Shapes - Problems on Circles Mensuration of 2D Shapes - Problems on Circles - Applications Mensuration of 2D Shapes - Problems on Circles - Case Studies Mensuration of 2D Shapes - Problems on Circles - Problem Set Mensuration of 2D Shapes - Problems on Triangles Mensuration of 2D Shapes - Problems on Triangles - Applications Mensuration of 2D Shapes - Problems on Triangles - Case Studies Mensuration of 2D Shapes - Problems on Triangles - Problem Set Mensuration of 2D Shapes - Proof-based Questions Mensuration of 2D Shapes - Proof-based Questions - Applications Mensuration of 2D Shapes - Proof-based Questions - Case Studies Mensuration of 2D Shapes - Proof-based Questions - Problem Set Quadrilaterals and Polygons Quadrilaterals and Polygons - Applications Quadrilaterals and Polygons - Case Studies Quadrilaterals and Polygons - Coordinate Geometry Applications Quadrilaterals and Polygons - Coordinate Geometry Applications - Applications Quadrilaterals and Polygons - Coordinate Geometry Applications - Case Studies Quadrilaterals and Polygons - Coordinate Geometry Applications - Problem Set Quadrilaterals and Polygons - Problem Set Quadrilaterals and Polygons - Problems on Circles Quadrilaterals and Polygons - Problems on Circles - Applications Quadrilaterals and Polygons - Problems on Circles - Case Studies Quadrilaterals and Polygons - Problems on Circles - Problem Set Quadrilaterals and Polygons - Problems on Triangles Quadrilaterals and Polygons - Problems on Triangles - Applications Quadrilaterals and Polygons - Problems on Triangles - Case Studies Quadrilaterals and Polygons - Problems on Triangles - Problem Set Quadrilaterals and Polygons - Proof-based Questions Quadrilaterals and Polygons - Proof-based Questions - Applications Quadrilaterals and Polygons - Proof-based Questions - Case Studies Quadrilaterals and Polygons - Proof-based Questions - Problem Set Similarity and Trigonometry Basics Similarity and Trigonometry Basics - Applications Similarity and Trigonometry Basics - Case Studies Similarity and Trigonometry Basics - Coordinate Geometry Applications Similarity and Trigonometry Basics - Coordinate Geometry Applications - Applications Similarity and Trigonometry Basics - Coordinate Geometry Applications - Case Studies Similarity and Trigonometry Basics - Coordinate Geometry Applications - Problem Set Similarity and Trigonometry Basics - Problem Set Similarity and Trigonometry Basics - Problems on Circles Similarity and Trigonometry Basics - Problems on Circles - Applications Similarity and Trigonometry Basics - Problems on Circles - Case Studies Similarity and Trigonometry Basics - Problems on Circles - Problem Set Similarity and Trigonometry Basics - Problems on Triangles Similarity and Trigonometry Basics - Problems on Triangles - Applications Similarity and Trigonometry Basics - Problems on Triangles - Case Studies Similarity and Trigonometry Basics - Problems on Triangles - Problem Set Similarity and Trigonometry Basics - Proof-based Questions Similarity and Trigonometry Basics - Proof-based Questions - Applications Similarity and Trigonometry Basics - Proof-based Questions - Case Studies Similarity and Trigonometry Basics - Proof-based Questions - Problem Set Triangles - Properties and Congruence Triangles - Properties and Congruence - Applications Triangles - Properties and Congruence - Case Studies Triangles - Properties and Congruence - Coordinate Geometry Applications Triangles - Properties and Congruence - Coordinate Geometry Applications - Applications Triangles - Properties and Congruence - Coordinate Geometry Applications - Case Studies Triangles - Properties and Congruence - Coordinate Geometry Applications - Problem Set Triangles - Properties and Congruence - Problem Set Triangles - Properties and Congruence - Problems on Circles Triangles - Properties and Congruence - Problems on Circles - Applications Triangles - Properties and Congruence - Problems on Circles - Case Studies Triangles - Properties and Congruence - Problems on Circles - Problem Set Triangles - Properties and Congruence - Problems on Triangles Triangles - Properties and Congruence - Problems on Triangles - Applications Triangles - Properties and Congruence - Problems on Triangles - Case Studies Triangles - Properties and Congruence - Problems on Triangles - Problem Set Triangles - Properties and Congruence - Proof-based Questions Triangles - Properties and Congruence - Proof-based Questions - Applications Triangles - Properties and Congruence - Proof-based Questions - Case Studies Triangles - Properties and Congruence - Proof-based Questions - Problem Set

Q. If the diameter of a circle is 14 cm, what is the circumference of the circle?

A. 22 cm
B. 28 cm
C. 44 cm
D. 14 cm

Solution

The circumference C of a circle is given by C = πd. Here, d = 14 cm, so C = π * 14 ≈ 43.98 cm, which rounds to 44 cm.

Correct Answer: B — 28 cm

Q. If the diameter of a circle is 14 cm, what is the circumference?

A. 44 cm
B. 28 cm
C. 22 cm
D. 14 cm

Solution

The circumference C of a circle is given by C = πd. Thus, C = π(14) ≈ 44 cm.

Correct Answer: A — 44 cm

Q. If the diameter of a circle is 14 cm, what is the circumference? (Use π = 22/7)

A. 44 cm
B. 28 cm
C. 22 cm
D. 14 cm

Solution

Circumference = πd = (22/7) * 14 = 44 cm.

Correct Answer: A — 44 cm

Q. If the diameter of a circle is 14 cm, what is the radius?

A. 7 cm
B. 14 cm
C. 21 cm
D. 28 cm

Solution

The radius is half of the diameter. Therefore, the radius is 14/2 = 7 cm.

Correct Answer: A — 7 cm

Q. If the diameter of a circle is 20 cm, what is the radius?

A. 5 cm
B. 10 cm
C. 15 cm
D. 20 cm

Solution

Radius = diameter/2 = 20/2 = 10 cm.

Correct Answer: B — 10 cm

Q. If the lengths of the sides of a triangle are 3 cm, 4 cm, and 5 cm, what is its perimeter?

A. 12 cm
B. 15 cm
C. 10 cm
D. 8 cm

Solution

Perimeter = 3 + 4 + 5 = 12 cm.

Correct Answer: A — 12 cm

Q. If the lengths of the sides of a triangle are 5 cm, 12 cm, and 13 cm, what type of triangle is it?

A. Acute
B. Obtuse
C. Right
D. Equilateral

Solution

Since 5² + 12² = 13², it is a right triangle.

Correct Answer: C — Right

Q. If the lengths of the sides of a triangle are 7 cm, 24 cm, and 25 cm, what is its area?

A. 84 cm²
B. 168 cm²
C. 42 cm²
D. 56 cm²

Solution

Using Heron's formula, s = (7 + 24 + 25)/2 = 28. Area = √(s(s-a)(s-b)(s-c)) = √(28(28-7)(28-24)(28-25)) = √(28*21*4*3) = 84 cm².

Correct Answer: A — 84 cm²

Q. If the lengths of the sides of a triangle are 7 cm, 24 cm, and 25 cm, what is the perimeter?

A. 56 cm
B. 50 cm
C. 45 cm
D. 30 cm

Solution

Perimeter = 7 + 24 + 25 = 56 cm.

Correct Answer: B — 50 cm

Q. If the lengths of the sides of a triangle are 7 cm, 24 cm, and 25 cm, what is the perimeter of the triangle?

A. 56 cm
B. 50 cm
C. 45 cm
D. 30 cm

Solution

Perimeter = 7 + 24 + 25 = 56 cm.

Correct Answer: B — 50 cm

Q. If the lengths of the sides of a triangle are in the ratio 3:4:5 and the perimeter is 60 cm, what is the length of the longest side?

A. 20 cm
B. 15 cm
C. 25 cm
D. 30 cm

Solution

Let the sides be 3x, 4x, 5x. Then, 3x + 4x + 5x = 60. Therefore, 12x = 60, x = 5. Longest side = 5x = 25 cm.

Correct Answer: A — 20 cm

Q. If the lengths of the sides of triangle ABC are 3 cm, 4 cm, and 5 cm, what type of triangle is it?

A. Equilateral
B. Isosceles
C. Scalene
D. Right

Solution

Triangle ABC is a right triangle because it satisfies the Pythagorean theorem: 3² + 4² = 5².

Correct Answer: D — Right

Q. If the lengths of the sides of triangle ABC are 7 cm, 24 cm, and 25 cm, is it a right triangle?

A. Yes
B. No
C. Only if angle A is 90 degrees
D. Only if angle B is 90 degrees

Solution

Yes, because 7² + 24² = 49 + 576 = 625 = 25², satisfying the Pythagorean theorem.

Correct Answer: A — Yes

Q. If the lengths of the sides of triangle ABC are in the ratio 3:4:5, what type of triangle is it?

A. Acute
B. Obtuse
C. Right
D. Equilateral

Solution

A triangle with sides in the ratio 3:4:5 is a right triangle, as it satisfies the Pythagorean theorem.

Correct Answer: C — Right

Q. If the lengths of the sides of triangle PQR are 7 cm, 24 cm, and 25 cm, what is the perimeter of triangle PQR?

A. 50 cm
B. 56 cm
C. 25 cm
D. 24 cm

Solution

The perimeter of a triangle is the sum of the lengths of its sides. Therefore, perimeter = 7 + 24 + 25 = 56 cm.

Correct Answer: A — 50 cm

Q. If the lengths of the sides of triangle PQR are in the ratio 3:4:5, what type of triangle is it?

A. Acute
B. Obtuse
C. Right
D. Equilateral

Solution

A triangle with sides in the ratio 3:4:5 is a right triangle, as it satisfies the Pythagorean theorem.

Correct Answer: C — Right

Q. If the lengths of the sides of triangle XYZ are 8 cm, 15 cm, and 17 cm, is it a right triangle?

A. Yes
B. No
C. It cannot be determined
D. Only if angle X is 90 degrees

Solution

Yes, because 8^2 + 15^2 = 64 + 225 = 289 = 17^2, satisfying the Pythagorean theorem.

Correct Answer: A — Yes

Q. If the lengths of two sides of a triangle are 5 cm and 12 cm, and the included angle is 90 degrees, what is the area?

A. 30 cm²
B. 60 cm²
C. 24 cm²
D. 20 cm²

Solution

Area = 1/2 * side1 * side2 = 1/2 * 5 * 12 = 30 cm².

Correct Answer: A — 30 cm²

Q. If the lengths of two sides of a triangle are 5 cm and 12 cm, what is the maximum possible length of the third side?

A. 16 cm
B. 17 cm
C. 18 cm
D. 19 cm

Solution

According to the triangle inequality theorem, the length of the third side must be less than the sum of the other two sides. Therefore, the maximum length is 5 + 12 = 17 cm.

Correct Answer: B — 17 cm

Q. If the lengths of two sides of a triangle are 5 cm and 12 cm, what is the range of possible lengths for the third side?

A. 1 cm to 17 cm
B. 6 cm to 16 cm
C. 7 cm to 12 cm
D. 5 cm to 12 cm

Solution

The length of the third side must be greater than the difference of the other two sides and less than their sum: |5 - 12| < third side < 5 + 12, which gives 7 cm < third side < 17 cm.

Correct Answer: B — 6 cm to 16 cm

Q. If the lengths of two sides of a triangle are 5 cm and 7 cm, what is the range of possible lengths for the third side?

A. 2 cm to 12 cm
B. 3 cm to 11 cm
C. 4 cm to 10 cm
D. 5 cm to 9 cm

Solution

The length of the third side must be greater than the difference of the other two sides and less than their sum: |5 - 7| < third side < 5 + 7, which gives 2 < third side < 12.

Correct Answer: B — 3 cm to 11 cm

Q. If the lengths of two sides of a triangle are 6 cm and 8 cm, what is the range of possible lengths for the third side?

A. 2 cm to 14 cm
B. 2 cm to 10 cm
C. 2 cm to 12 cm
D. 2 cm to 8 cm

Solution

The length of the third side must be greater than the difference of the other two sides and less than their sum: |6 - 8| < third side < 6 + 8, which gives 2 cm < third side < 14 cm.

Correct Answer: B — 2 cm to 10 cm

Q. If the lengths of two sides of a triangle are 8 cm and 15 cm, and the included angle is 60 degrees, what is the area?

A. 60 cm²
B. 80 cm²
C. 90 cm²
D. 100 cm²

Solution

Area = 1/2 * a * b * sin(C) = 1/2 * 8 * 15 * sin(60) = 60 cm².

Correct Answer: A — 60 cm²

Q. If the lengths of two sides of a triangle are 8 cm and 6 cm, what is the range of possible lengths for the third side?

A. 2 cm to 14 cm
B. 2 cm to 10 cm
C. 4 cm to 14 cm
D. 4 cm to 10 cm

Solution

The length of the third side must be greater than the difference of the other two sides and less than their sum: |8 - 6| < third side < 8 + 6, which gives 2 < third side < 14.

Correct Answer: B — 2 cm to 10 cm

Q. If the perimeter of an equilateral triangle is 36 cm, what is the length of one side?

A. 10 cm
B. 12 cm
C. 9 cm
D. 15 cm

Solution

Perimeter = 3 * side. Therefore, side = Perimeter / 3 = 36 / 3 = 12 cm.

Correct Answer: B — 12 cm

Q. If the radius of a circle is 5 cm, what is the circumference of the circle?

A. 10π cm
B. 15π cm
C. 20π cm
D. 25π cm

Solution

The circumference of a circle is given by the formula C = 2πr. Thus, C = 2π(5) = 10π cm.

Correct Answer: A — 10π cm

Q. If the radius of a circle is 5, what is the area of the circle?

A. 25π
B. 20π
C. 30π
D. 15π

Solution

The area of a circle is given by A = πr^2. Therefore, A = π(5^2) = 25π.

Correct Answer: A — 25π

Q. If the radius of a circle is 7 cm, what is the area of the circle?

A. 154 cm²
B. 49 cm²
C. 28 cm²
D. 44 cm²

Solution

The area of a circle is given by the formula A = πr². Thus, A = π(7)² = 49π ≈ 154 cm².

Correct Answer: A — 154 cm²

Q. If the radius of a circle is 7 cm, what is the circumference of the circle?

A. 14π cm
B. 21π cm
C. 28π cm
D. 49π cm

Solution

The circumference of a circle is calculated using the formula 2πr. Therefore, circumference = 2π × 7 cm = 14π cm.

Correct Answer: B — 21π cm

Q. If the radius of a circle is 7 cm, what is the circumference?

A. 14π cm
B. 21π cm
C. 28π cm
D. 49π cm

Solution

The circumference of a circle is calculated using the formula 2πr. Thus, the circumference is 2π × 7 cm = 14π cm.

Correct Answer: B — 21π cm

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