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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 - 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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. In a triangle, if one angle measures 50 degrees and the other two angles are equal, what is the measure of each of the equal angles?

A. 65 degrees
B. 70 degrees
C. 80 degrees
D. 90 degrees

Solution

The sum of angles in a triangle is 180 degrees. Let x be the measure of each equal angle: 50 + 2x = 180, so 2x = 130, thus x = 65 degrees.

Correct Answer: B — 70 degrees

Q. In a triangle, if one angle measures 60 degrees and the other measures 70 degrees, what is the measure of the third angle?

A. 50 degrees
B. 60 degrees
C. 70 degrees
D. 80 degrees

Solution

The third angle can be found by subtracting the sum of the other two angles from 180 degrees: 180 - (60 + 70) = 50 degrees.

Correct Answer: D — 80 degrees

Q. In a triangle, if one angle measures 70 degrees and another measures 50 degrees, what is the measure of the third angle?

A. 60 degrees
B. 70 degrees
C. 80 degrees
D. 90 degrees

Solution

The sum of angles in a triangle is 180 degrees. Therefore, the third angle is 180 - 70 - 50 = 60 degrees.

Correct Answer: A — 60 degrees

Q. In a triangle, if one angle measures 70 degrees and the other measures 50 degrees, what is the measure of the third angle?

A. 60 degrees
B. 70 degrees
C. 80 degrees
D. 90 degrees

Solution

The sum of the angles in a triangle is 180 degrees. Therefore, the third angle is 180 - 70 - 50 = 60 degrees.

Correct Answer: C — 80 degrees

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

A. Yes
B. No
C. Cannot be determined
D. Only if angles are known

Solution

To determine if it is a right triangle, we can use the Pythagorean theorem. Here, 25² = 7² + 24², which simplifies to 625 = 49 + 576, thus 625 = 625. Therefore, it is a right triangle.

Correct Answer: A — Yes

Q. In a triangle, if the lengths of the sides are 7 cm, 24 cm, and 25 cm, what type of triangle is it?

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

Solution

This triangle is a right triangle because 7² + 24² = 25² (49 + 576 = 625).

Correct Answer: C — Right

Q. In a triangle, if the lengths of two sides 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

By the triangle inequality theorem, the maximum length of the third side is less than the sum of the other two sides: 5 + 12 = 17 cm.

Correct Answer: B — 17 cm

Q. In a triangle, if the lengths of two sides are 7 cm and 24 cm, what is the minimum possible length of the third side?

A. 1 cm
B. 17 cm
C. 18 cm
D. 31 cm

Solution

By the triangle inequality theorem, the length of the third side must be greater than the difference of the other two sides. Therefore, the minimum length = 24 - 7 = 17 cm.

Correct Answer: B — 17 cm

Q. In a triangle, if the lengths of two sides are 8 cm and 15 cm, what is the maximum possible length of the third side?

A. 22 cm
B. 23 cm
C. 24 cm
D. 25 cm

Solution

The maximum length of the third side is less than the sum of the other two sides: 8 + 15 = 23 cm, so the maximum possible length is 22 cm.

Correct Answer: A — 22 cm

Q. In a triangle, if two angles are 45 degrees and 55 degrees, what is the measure of the third angle?

A. 80 degrees
B. 90 degrees
C. 100 degrees
D. 110 degrees

Solution

The sum of the angles in a triangle is always 180 degrees. Therefore, the third angle = 180 - (45 + 55) = 180 - 100 = 80 degrees.

Correct Answer: B — 90 degrees

Q. In a triangle, if two angles are 45 degrees and 55 degrees, what is the measure of the angle formed by a line parallel to one side of the triangle and the extension of the other side?

A. 80 degrees
B. 45 degrees
C. 55 degrees
D. 100 degrees

Solution

The third angle of the triangle is 80 degrees. The angle formed by the parallel line and the extension of the other side is equal to this angle due to the Corresponding Angles Postulate.

Correct Answer: A — 80 degrees

Q. In a triangle, if two angles are 45 degrees and 55 degrees, what is the third angle?

A. 80 degrees
B. 90 degrees
C. 100 degrees
D. 110 degrees

Solution

The sum of the angles in a triangle is always 180 degrees. Therefore, the third angle = 180 - (45 + 55) = 180 - 100 = 80 degrees.

Correct Answer: B — 90 degrees

Q. In a triangle, if two angles are 45 degrees and 55 degrees, what type of triangle is it?

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

Solution

Since all angles are less than 90 degrees, the triangle is acute.

Correct Answer: A — Acute

Q. In a triangle, if two angles are 45 degrees each, what is the measure of the third angle?

A. 45 degrees
B. 60 degrees
C. 90 degrees
D. 75 degrees

Solution

The sum of the angles in a triangle is always 180 degrees. If two angles are 45 degrees each, the third angle is 180 - (45 + 45) = 90 degrees.

Correct Answer: C — 90 degrees

Q. In a triangle, if two angles are 50 degrees and 60 degrees, what is the measure of the third angle?

A. 70 degrees
B. 80 degrees
C. 90 degrees
D. 100 degrees

Solution

The sum of angles in a triangle is 180 degrees. Therefore, the third angle is 180 - (50 + 60) = 70 degrees.

Correct Answer: B — 80 degrees

Q. In a triangle, if two angles are equal and one measures 50 degrees, what is the measure of the third angle?

A. 50 degrees
B. 80 degrees
C. 100 degrees
D. 60 degrees

Solution

Let the equal angles be x. Then, 2x + 50 = 180. Solving gives x = 65 degrees, so the third angle is 180 - 2(50) = 80 degrees.

Correct Answer: B — 80 degrees

Q. In a triangle, if two angles are equal and the third angle measures 40 degrees, what is the measure of each of the equal angles?

A. 70 degrees
B. 40 degrees
C. 20 degrees
D. 60 degrees

Solution

Let each equal angle be x. The sum of angles in a triangle is 180 degrees, so 2x + 40 = 180. Thus, 2x = 140, giving x = 70 degrees.

Correct Answer: A — 70 degrees

Q. In a triangle, if two angles measure 45 degrees and 55 degrees, what is the measure of the third angle?

A. 80 degrees
B. 90 degrees
C. 100 degrees
D. 110 degrees

Solution

The sum of the angles in a triangle is always 180 degrees. Therefore, the third angle = 180 - (45 + 55) = 80 degrees.

Correct Answer: B — 90 degrees

Q. In a triangle, if two angles measure 45 degrees each, what is the measure of the third angle?

A. 90 degrees
B. 45 degrees
C. 60 degrees
D. 30 degrees

Solution

The sum of angles in a triangle is 180 degrees. Therefore, the third angle is 180 - 45 - 45 = 90 degrees.

Correct Answer: A — 90 degrees

Q. In a triangle, if two angles measure 45 degrees each, what type of triangle is it?

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

Solution

A triangle with two equal angles is an isosceles triangle. Since two angles measure 45 degrees, it is isosceles.

Correct Answer: B — Isosceles

Q. In a triangle, if two angles measure 50 degrees and 60 degrees, what is the measure of the third angle?

A. 70 degrees
B. 80 degrees
C. 90 degrees
D. 100 degrees

Solution

The sum of angles in a triangle is 180 degrees. Therefore, the third angle = 180 - (50 + 60) = 70 degrees.

Correct Answer: B — 80 degrees

Q. In a triangle, if two sides are 7 units and 24 units, what is the maximum possible length of the third side?

A. 30 units
B. 25 units
C. 31 units
D. 32 units

Solution

The maximum length of the third side is less than the sum of the other two sides: 7 + 24 = 31 units.

Correct Answer: B — 25 units

Q. In an equilateral triangle with a side length of 6 cm, what is the area?

A. 9√3 cm²
B. 12 cm²
C. 18 cm²
D. 36 cm²

Solution

Area = (√3/4) * side² = (√3/4) * 6² = 9√3 cm².

Correct Answer: A — 9√3 cm²

Q. In an equilateral triangle, if one side measures 12 cm, what is the area of the triangle?

A. 36√3 cm²
B. 24 cm²
C. 48 cm²
D. 144 cm²

Solution

The area of an equilateral triangle is given by the formula: Area = (√3/4) * side² = (√3/4) * 12² = 36√3 cm².

Correct Answer: A — 36√3 cm²

Q. In an isosceles triangle, if the equal sides are each 10 cm and the base is 12 cm, what is the height of the triangle?

A. 8 cm
B. 6 cm
C. 5 cm
D. 4 cm

Solution

Using the Pythagorean theorem, the height can be found by splitting the triangle in half: height = √(10^2 - 6^2) = √(100 - 36) = √64 = 8 cm.

Correct Answer: B — 6 cm

Q. In circle O, if the radius is 5 cm, what is the circumference?

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

Solution

Circumference of a circle is given by C = 2πr. Therefore, C = 2π(5) = 10π cm.

Correct Answer: A — 10π cm

Q. In coordinate geometry, what is the distance between the points (1, 2) and (4, 6)?

A. 5
B. 3
C. 4
D. 7

Solution

Distance = √((4-1)² + (6-2)²) = √(3² + 4²) = √(9 + 16) = √25 = 5.

Correct Answer: A — 5

Q. In coordinate geometry, what is the distance between the points (3, 4) and (7, 1)?

A. 5
B. 4
C. 3
D. 6

Solution

Using the distance formula, d = √((x2 - x1)² + (y2 - y1)²) = √((7 - 3)² + (1 - 4)²) = √(16 + 9) = √25 = 5.

Correct Answer: A — 5

Q. In coordinate geometry, what is the midpoint of the segment connecting points (2, 3) and (4, 7)?

A. (3, 5)
B. (2, 5)
C. (4, 3)
D. (5, 7)

Solution

The midpoint M of a segment with endpoints (x1, y1) and (x2, y2) is given by M = ((x1 + x2)/2, (y1 + y2)/2) = ((2 + 4)/2, (3 + 7)/2) = (3, 5).

Correct Answer: A — (3, 5)

Q. In coordinate geometry, what is the slope of a line that is parallel to the line represented by the equation y = 3x + 2?

A. 3
B. 2
C. 1/3
D. 0

Solution

Parallel lines have the same slope. The slope of the given line is 3.

Correct Answer: A — 3

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