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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!

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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 a parallelogram has vertices at (0, 0), (2, 3), (5, 3), and (3, 0), what is its area?

A. 6
B. 8
C. 10
D. 12

Solution

The area of a parallelogram can be calculated using the formula: Area = base * height. The base is 5 - 0 = 5 and the height is 3. Therefore, area = 5 * 3 = 15.

Correct Answer: B — 8

Q. If a parallelogram has vertices at (2, 3), (5, 3), (6, 1), and (3, 1), what is its area?

A. 6
B. 8
C. 10
D. 12

Solution

Base = 5 - 2 = 3, Height = 3 - 1 = 2. Area = base * height = 3 * 2 = 6.

Correct Answer: B — 8

Q. If a point P divides the line segment joining A(2, 3) and B(8, 7) in the ratio 1:3, what are the coordinates of point P?

A. (5, 5)
B. (4, 4)
C. (6, 6)
D. (3, 3)

Solution

Using the section formula: P = ((mx2 + nx1)/(m+n), (my2 + ny1)/(m+n)) where m=1, n=3, A(2,3), B(8,7). P = ((1*8 + 3*2)/(1+3), (1*7 + 3*3)/(1+3)) = (5, 5).

Correct Answer: A — (5, 5)

Q. If a point P divides the line segment joining A(2, 3) and B(8, 7) in the ratio 3:1, what are the coordinates of P?

A. (5, 4)
B. (6, 5)
C. (7, 6)
D. (4, 5)

Solution

Using the section formula: P = ((3*8 + 1*2)/(3+1), (3*7 + 1*3)/(3+1)) = (6, 5).

Correct Answer: B — (6, 5)

Q. If a point P divides the segment joining A(1, 2) and B(5, 6) in the ratio 3:1, what are the coordinates of P?

A. (3, 4)
B. (4, 5)
C. (2.5, 3.5)
D. (3.5, 4.5)

Solution

Using the section formula: P = ((mx2 + nx1)/(m+n), (my2 + ny1)/(m+n)) = ((3*5 + 1*1)/(3+1), (3*6 + 1*2)/(3+1)) = (3.5, 4.5).

Correct Answer: D — (3.5, 4.5)

Q. If a point P divides the segment joining A(2, 1) and B(8, 5) in the ratio 3:1, what are the coordinates of P?

A. (5, 3)
B. (6, 4)
C. (4, 2)
D. (3, 2)

Solution

Using the section formula: P = ((3*8 + 1*2)/(3+1), (3*5 + 1*1)/(3+1)) = (5, 3).

Correct Answer: A — (5, 3)

Q. If a point P divides the segment joining A(2, 3) and B(8, 7) in the ratio 3:1, what are the coordinates of P?

A. (5, 4)
B. (6, 5)
C. (7, 6)
D. (4, 5)

Solution

Using the section formula: P = ((3*8 + 1*2)/(3+1), (3*7 + 1*3)/(3+1)) = (6, 5).

Correct Answer: B — (6, 5)

Q. If a polygon has 5 sides, what is it called?

A. Triangle
B. Quadrilateral
C. Pentagon
D. Hexagon

Solution

A polygon with 5 sides is called a pentagon.

Correct Answer: C — Pentagon

Q. If a polygon has 8 sides, what is it called?

A. Hexagon
B. Heptagon
C. Octagon
D. Nonagon

Solution

A polygon with 8 sides is called an octagon.

Correct Answer: C — Octagon

Q. If a quadrilateral has angles measuring 90 degrees, 85 degrees, 95 degrees, and x degrees, what is the value of x?

A. 90 degrees
B. 80 degrees
C. 85 degrees
D. 75 degrees

Solution

The sum of the interior angles of a quadrilateral is 360 degrees. Therefore, x = 360 - (90 + 85 + 95) = 360 - 270 = 90 degrees.

Correct Answer: D — 75 degrees

Q. If a quadrilateral has sides of lengths 5 cm, 12 cm, 13 cm, and 14 cm, is it a cyclic quadrilateral?

A. Yes
B. No
C. Not enough information
D. Only if it is a rectangle

Solution

A quadrilateral is cyclic if the sum of opposite angles is 180 degrees. The given side lengths do not provide enough information to determine if it is cyclic.

Correct Answer: B — No

Q. If a quadrilateral has two pairs of opposite sides that are equal, what can be concluded about the quadrilateral?

A. It is a rectangle
B. It is a rhombus
C. It is a parallelogram
D. It is a trapezoid

Solution

A quadrilateral with two pairs of opposite sides that are equal is a parallelogram by definition.

Correct Answer: C — It is a parallelogram

Q. If a quadrilateral has two pairs of opposite sides that are equal, what type of quadrilateral is it?

A. Rectangle
B. Rhombus
C. Trapezoid
D. Parallelogram

Solution

A quadrilateral with two pairs of opposite sides that are equal is classified as a parallelogram.

Correct Answer: D — Parallelogram

Q. If a quadrilateral is a kite, what can be said about its diagonals?

A. They are equal
B. They bisect each other
C. One diagonal bisects the other
D. They are perpendicular

Solution

In a kite, one diagonal bisects the other diagonal.

Correct Answer: C — One diagonal bisects the other

Q. If a quadrilateral is a rectangle, what can be said about its diagonals?

A. They are equal and bisect each other
B. They are unequal
C. They are perpendicular
D. They are parallel

Solution

In a rectangle, the diagonals are equal in length and bisect each other.

Correct Answer: A — They are equal and bisect each other

Q. If a quadrilateral is a rectangle, which of the following statements is true?

A. All sides are equal
B. Opposite sides are equal
C. All angles are acute
D. Diagonals are perpendicular

Solution

In a rectangle, opposite sides are equal in length.

Correct Answer: B — Opposite sides are equal

Q. If a rectangle has a perimeter of 30 cm and a length of 10 cm, what is its width?

A. 5 cm
B. 7.5 cm
C. 10 cm
D. 12.5 cm

Solution

Perimeter = 2(length + width), so 30 cm = 2(10 cm + width). Width = (30 cm/2) - 10 cm = 5 cm.

Correct Answer: B — 7.5 cm

Q. If a rectangle has vertices at (1, 1), (1, 4), (5, 1), and (5, 4), what is its area?

A. 12
B. 16
C. 20
D. 24

Solution

The area of a rectangle is given by the formula: Area = length * width. The length is 5 - 1 = 4 and the width is 4 - 1 = 3. Thus, Area = 4 * 3 = 12.

Correct Answer: B — 16

Q. If a rectangle's length is doubled and its width is halved, what happens to its area?

A. It remains the same
B. It doubles
C. It halves
D. It quadruples

Solution

New area = (2 * length) * (width/2) = length * width = original area, so it doubles.

Correct Answer: B — It doubles

Q. If a regular hexagon has a side length of 3 cm, what is the perimeter of the hexagon?

A. 9 cm
B. 12 cm
C. 15 cm
D. 18 cm

Solution

The perimeter of a regular hexagon is calculated as 6 times the side length. Therefore, perimeter = 6 × 3 cm = 18 cm.

Correct Answer: D — 18 cm

Q. If a regular hexagon has a side length of 6 cm, what is its perimeter?

A. 24 cm
B. 30 cm
C. 36 cm
D. 42 cm

Solution

The perimeter of a regular hexagon is calculated as P = 6 * side length. Here, P = 6 * 6 cm = 36 cm.

Correct Answer: C — 36 cm

Q. If a regular hexagon has a side length of 6 cm, what is the perimeter of the hexagon?

A. 24 cm
B. 30 cm
C. 36 cm
D. 42 cm

Solution

The perimeter of a regular hexagon is calculated as 6 times the side length. Therefore, perimeter = 6 × 6 cm = 36 cm.

Correct Answer: C — 36 cm

Q. If a rhombus has diagonals of lengths 10 and 24, what is its area?

A. 120
B. 140
C. 160
D. 180

Solution

Area = (d1 * d2) / 2 = (10 * 24) / 2 = 120.

Correct Answer: A — 120

Q. If a square has a perimeter of 32 cm, what is the area of the square?

A. 64 cm²
B. 128 cm²
C. 16 cm²
D. 32 cm²

Solution

Side length = perimeter/4 = 32/4 = 8 cm. Area = side² = 8² = 64 cm².

Correct Answer: A — 64 cm²

Q. If a square has a perimeter of 40 cm, what is the area of the square?

A. 100 cm²
B. 160 cm²
C. 200 cm²
D. 250 cm²

Solution

Side length = perimeter/4 = 40/4 = 10 cm. Area = side² = 10² = 100 cm².

Correct Answer: A — 100 cm²

Q. If a square has a perimeter of 40 cm, what is the length of one side?

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

Solution

The perimeter of a square is calculated as 4 times the side length. Therefore, if the perimeter is 40 cm, then side length = 40 cm / 4 = 10 cm.

Correct Answer: B — 10 cm

Q. If a square has a side length of 4 cm, what is its area?

A. 16 cm²
B. 12 cm²
C. 8 cm²
D. 20 cm²

Solution

The area of a square is given by the formula: Area = side². Here, side = 4 cm. Area = 4² = 16 cm².

Correct Answer: A — 16 cm²

Q. If a square has a side length of 5 cm, what is its area?

A. 20 cm²
B. 25 cm²
C. 30 cm²
D. 15 cm²

Solution

The area of a square is given by the formula: Area = side². Here, Area = 5² = 25 cm².

Correct Answer: B — 25 cm²

Q. If a tangent and a chord intersect at a point on the circle, what is the relationship between the angle formed and the angle subtended by the chord at the opposite arc?

A. They are equal
B. The tangent angle is double
C. The chord angle is double
D. They are supplementary

Solution

The angle formed by the tangent and the chord is equal to the angle subtended by the chord at the opposite arc.

Correct Answer: A — They are equal

Q. If a tangent and a radius meet at a point on the circle, what is the angle between them?

A. 90 degrees
B. 45 degrees
C. 180 degrees
D. 0 degrees

Solution

The tangent to a circle at any point is perpendicular to the radius at that point, forming a 90-degree angle.

Correct Answer: A — 90 degrees

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