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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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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 triangle STU, if angle S = 30 degrees and angle T = 70 degrees, what is the length of side SU if ST = 10 cm and TU = 15 cm?

A. 7.5 cm
B. 10 cm
C. 12.5 cm
D. 15 cm

Solution

Using the Law of Sines: SU / sin(80) = 10 / sin(30). Therefore, SU = 10 * sin(80) / sin(30) = 10 * 0.9848 / 0.5 = 19.696 cm.

Correct Answer: C — 12.5 cm

Q. In triangle STU, if angle S = 45 degrees and angle T = 45 degrees, what is the type of triangle STU?

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

Solution

Since two angles are equal, triangle STU is isosceles.

Correct Answer: D — Isosceles

Q. In triangle STU, if ST = 12 cm, TU = 16 cm, and SU = 20 cm, what is the perimeter of triangle STU?

A. 28 cm
B. 36 cm
C. 40 cm
D. 48 cm

Solution

The perimeter of triangle STU is ST + TU + SU = 12 + 16 + 20 = 48 cm.

Correct Answer: B — 36 cm

Q. In triangle STU, if ST = 7 cm, TU = 24 cm, and SU = 25 cm, is triangle STU a right triangle?

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

Solution

Using the Pythagorean theorem, 7^2 + 24^2 = 49 + 576 = 625, which equals 25^2. Therefore, triangle STU is a right triangle.

Correct Answer: A — Yes

Q. In triangle UVW, if angle U = 45 degrees and angle V = 45 degrees, what type of triangle is it?

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

Solution

Since two angles are equal (45 degrees each), triangle UVW is an isosceles triangle.

Correct Answer: B — Isosceles

Q. In triangle XYZ, if angle X = 45 degrees and angle Y = 45 degrees, what type of triangle is it?

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

Solution

Since two angles are equal, triangle XYZ is an isosceles triangle.

Correct Answer: B — Isosceles

Q. In triangle XYZ, if angle X = 90 degrees, angle Y = 45 degrees, and side XY = 10 units, what is the length of side XZ?

A. 10√2 units
B. 5√2 units
C. 10 units
D. 5 units

Solution

In a 45-45-90 triangle, the sides opposite the 45-degree angles are equal, and the hypotenuse is √2 times the length of each leg. Thus, XZ = XY√2 = 10√2 units.

Correct Answer: A — 10√2 units

Q. In triangle XYZ, if angle X is 30 degrees and angle Y is 60 degrees, what is angle Z?

A. 30 degrees
B. 60 degrees
C. 90 degrees
D. 120 degrees

Solution

The sum of the angles in a triangle is 180 degrees. Therefore, angle Z = 180 - (30 + 60) = 90 degrees.

Correct Answer: C — 90 degrees

Q. In triangle XYZ, if XY = 5 cm, YZ = 12 cm, and XZ = 13 cm, is triangle XYZ a right triangle?

A. Yes
B. No
C. Not enough information
D. Only if XY is the longest side

Solution

Triangle XYZ is a right triangle because 5² + 12² = 25 + 144 = 169 = 13².

Correct Answer: A — Yes

Q. In triangle XYZ, if XY = 7 cm, YZ = 24 cm, and XZ = 25 cm, is triangle XYZ a right triangle?

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

Solution

Using the Pythagorean theorem, 7^2 + 24^2 = 49 + 576 = 625 = 25^2, thus triangle XYZ is a right triangle.

Correct Answer: A — Yes

Q. In triangle XYZ, if XY = 8 cm, XZ = 6 cm, and YZ = 10 cm, what type of triangle is it?

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

Solution

Triangle XYZ is scalene because all sides have different lengths.

Correct Answer: C — Scalene

Q. In triangle XYZ, if XY = 8 cm, XZ = 6 cm, and YZ = 10 cm, which side is the longest?

A. XY
B. XZ
C. YZ
D. All sides are equal

Solution

YZ is the longest side since 10 cm is greater than both 8 cm and 6 cm.

Correct Answer: C — YZ

Q. In triangle XYZ, if XY = 8 cm, YZ = 6 cm, and XZ = 10 cm, what type of triangle is it?

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

Solution

Triangle XYZ has all sides of different lengths (8 cm, 6 cm, 10 cm), so it is a scalene triangle.

Correct Answer: C — Scalene

Q. In triangle XYZ, if XY = 8, YZ = 6, and XZ = 10, what type of triangle is it?

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

Solution

Triangle XYZ is a right triangle because 8^2 + 6^2 = 10^2.

Correct Answer: D — Right

Q. In triangle XYZ, if XY = 8, YZ = 6, and XZ = 10, which side is the longest?

A. XY
B. YZ
C. XZ
D. All sides are equal

Solution

The longest side in triangle XYZ is XZ, which measures 10 units.

Correct Answer: C — XZ

Q. Triangle DEF is similar to triangle XYZ. If the lengths of DE and XY are 4 cm and 8 cm respectively, what is the ratio of the areas of the triangles?

A. 1:2
B. 1:4
C. 1:8
D. 1:16

Solution

The ratio of the areas of similar triangles is the square of the ratio of their corresponding sides. (4/8)^2 = 1/4.

Correct Answer: B — 1:4

Q. Triangle DEF is similar to triangle XYZ. If the sides of triangle DEF are 3 cm, 4 cm, and 5 cm, what is the length of the longest side of triangle XYZ if its shortest side is 6 cm?

A. 8 cm
B. 9 cm
C. 10 cm
D. 12 cm

Solution

The ratio of the sides of similar triangles is constant. The shortest side ratio is 6/3 = 2. Therefore, the longest side of triangle XYZ = 5 * 2 = 10 cm.

Correct Answer: C — 10 cm

Q. Triangle GHI is an isosceles triangle with GH = GI and angle H = 30 degrees. What is the measure of angle I?

A. 30 degrees
B. 60 degrees
C. 75 degrees
D. 90 degrees

Solution

In an isosceles triangle, the base angles are equal. Therefore, angle G + angle I = 150 degrees. Each angle = 60 degrees.

Correct Answer: B — 60 degrees

Q. Two chords AB and CD of a circle intersect at point E. If AE = 3 cm, EB = 5 cm, and CE = 4 cm, what is the length of ED?

A. 6 cm
B. 8 cm
C. 5 cm
D. 7 cm

Solution

Using the intersecting chords theorem: AE * EB = CE * ED, we have 3 * 5 = 4 * ED, thus ED = 15/4 = 3.75 cm.

Correct Answer: B — 8 cm

Q. Two circles are tangent to each other. If the radius of the first circle is 3 cm and the second is 5 cm, what is the distance between their centers?

A. 2 cm
B. 8 cm
C. 3 cm
D. 5 cm

Solution

The distance between the centers of two tangent circles is the sum of their radii: 3 cm + 5 cm = 8 cm.

Correct Answer: B — 8 cm

Q. Two circles have radii of 3 cm and 5 cm. What is the distance between their centers if they are externally tangent?

A. 2 cm
B. 8 cm
C. 5 cm
D. 3 cm

Solution

Distance = r1 + r2 = 3 + 5 = 8 cm.

Correct Answer: B — 8 cm

Q. Two circles intersect at points A and B. If the angle ∠AOB is 60°, what is the measure of the angle ∠APB where P is any point on the circumference of the circles?

A. 30°
B. 60°
C. 90°
D. 120°

Solution

Angle ∠APB = 1/2 ∠AOB = 1/2(60°) = 30°.

Correct Answer: A — 30°

Q. Two circles intersect at points A and B. If the angle ∠APB is 60°, what is the measure of the angle ∠AOB, where O is the center of the circle?

A. 30°
B. 60°
C. 120°
D. 90°

Solution

The angle at the center is twice the angle at the circumference, so ∠AOB = 2 * ∠APB = 2 * 60° = 120°.

Correct Answer: C — 120°

Q. Two circles intersect at points A and B. If the line segment AB is the common chord, what can be said about the perpendicular from the center of either circle to AB?

A. It bisects AB
B. It is equal to AB
C. It is longer than AB
D. It is shorter than AB

Solution

The perpendicular from the center of a circle to a chord bisects the chord.

Correct Answer: A — It bisects AB

Q. Two circles intersect at points A and B. If the radius of the first circle is 4 cm and the second circle is 6 cm, what is the maximum distance between the centers of the circles?

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

Solution

Maximum distance = r1 + r2 = 4 + 6 = 10 cm.

Correct Answer: A — 10 cm

Q. Two circles intersect at points A and B. If the radius of the first circle is 4 cm and the second is 6 cm, what is the maximum distance between the centers of the circles?

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

Solution

Maximum distance = r1 + r2 = 4 + 6 = 10 cm.

Correct Answer: A — 10 cm

Q. Two circles intersect at points A and B. If the radius of the first circle is 5 cm and the second is 3 cm, what is the maximum distance between the centers of the circles?

A. 8 cm
B. 10 cm
C. 6 cm
D. 7 cm

Solution

Maximum distance = r1 + r2 = 5 + 3 = 8 cm.

Correct Answer: A — 8 cm

Q. Two circles intersect at points A and B. What is the relationship between the angles ∠AOB and ∠APB, where O is the center of one circle and P is the center of the other?

A. ∠AOB = ∠APB
B. ∠AOB = 2∠APB
C. ∠AOB = ½∠APB
D. ∠AOB + ∠APB = 180 degrees

Solution

The angle ∠AOB is twice the angle ∠APB because of the inscribed angle theorem, which states that the angle at the center is twice the angle at the circumference.

Correct Answer: B — ∠AOB = 2∠APB

Q. Two lines are parallel, and a transversal intersects them, creating angles of 75 degrees and x degrees. What is the value of x?

A. 75 degrees
B. 105 degrees
C. 180 degrees
D. 90 degrees

Solution

The angles are supplementary, so x = 180 - 75 = 105 degrees.

Correct Answer: B — 105 degrees

Q. Two parallel lines are cut by a transversal, creating angles of 120 degrees and x degrees. What is the value of x?

A. 60 degrees
B. 120 degrees
C. 180 degrees
D. 30 degrees

Solution

The angles formed are supplementary. Therefore, 120 + x = 180, which gives x = 60 degrees.

Correct Answer: A — 60 degrees

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