Preparing for exams becomes much easier when you regularly practice chapter-wise objective questions. Find chapter-wise Class 7 Maths Chapter 9 Geometric Twins MCQ Questions and Answers aligned with the latest CBSE Board syllabus. These questions will help you strengthen your understanding of geometric concepts, improve problem-solving skills, and assess your preparation before unit tests, half-yearly examinations, and annual exams.
The MCQs cover all the important concepts from Chapter 9, including points, lines, line segments, rays, angles, parallel lines, perpendicular lines, and other fundamental geometric ideas introduced in the chapter. Each question will include the correct answer along with a brief explanation to help you understand the concept instead of simply memorizing the answer. After completing the MCQs, you can quickly revise the chapter using the Quick Revision Notes available below.
If you're looking to practice more objective questions, explore our complete collection of Class 7 MCQs covering all subjects. For additional mathematics practice, visit our Class 7 Maths MCQs page, where you'll find chapter-wise questions based on the latest CBSE curriculum. You can also browse all subject-wise MCQs to strengthen your exam preparation with structured practice.
Class 7 Maths Chapter 9 Geometric Twins MCQs with Answers and Explanations
Strengthen your understanding of congruence by practicing these Class 7 Maths Chapter 9 Geometric Twins MCQs with Answers. The questions below cover the most important concepts from the chapter, including congruent figures, transformations, congruence criteria, corresponding parts, and CPCT. Attempt each question before checking the answer and explanation to improve your conceptual understanding and exam readiness.
Q. What is meant by geometric twins in mathematics?
A. Figures that have the same area but different shapes
B. Figures that have the same shape and exactly the same size
C. Figures with equal perimeters only
D. Figures having the same number of sides
Answer:B
Explanation: Geometric twins are figures that are congruent, meaning they match perfectly in both shape and size. If one figure is placed over the other, they overlap completely without any gap or mismatch. Having only the same area, perimeter, or number of sides is not enough to establish congruence.
Q. Which mathematical symbol is used to represent congruence?
A. ≈
B. ∼
C. =
D. ≅
Answer:D
Explanation: The symbol ≅ is used to show that two geometric figures are congruent. It indicates that the figures have identical shape and size. Symbols like "=" represent equality of values, while "∼" is commonly used to denote similarity rather than congruence.
Q. Which of the following transformations keeps two congruent figures as geometric twins?
A. Rotation only
B. Translation only
C. Reflection only
D. Rotation, translation and reflection
Answer:D
Explanation: Congruent figures remain unchanged in size and shape even after rotating, sliding (translation), or flipping (reflection). These transformations only change the position or orientation of the figure without affecting its measurements, so the figures continue to be geometric twins.
Q. Two line segments can be called congruent when they have:
A. The same direction
B. Equal length
C. The same colour
D. Equal thickness
Answer:B
Explanation: Congruence of line segments depends only on their length. Two segments may be drawn in different directions or positions, but if their lengths are equal, they are considered congruent. Their appearance or orientation does not affect congruence.
Q. Two circles are congruent if they have the same:
A. Diameter only
B. Circumference only
C. Radius
D. Centre
Answer:C
Explanation: The radius completely determines the size of a circle. Therefore, two circles with equal radii are congruent because they have identical dimensions. Their centres may be at different locations, but that does not change their congruence.
Q. Which condition makes two rectangles congruent?
A. Equal area only
B. Equal perimeter only
C. Equal length and equal breadth
D. Equal diagonals only
Answer:C
Explanation: For two rectangles to be congruent, both their corresponding lengths and breadths must be equal. Rectangles having the same area or perimeter can still have different dimensions, so those conditions alone do not guarantee congruence.
Q. Which of the following is NOT a valid criterion for triangle congruence?
A. SSS
B. SAS
C. ASA
D. AAA
Answer:D
Explanation: Although triangles with equal corresponding angles have the same shape, they may differ in size. Therefore, AAA proves similarity, not congruence. The valid congruence criteria introduced in this chapter are SSS, SAS, ASA, and RHS.
Q. According to the SSS congruence rule, two triangles are congruent when:
A. One side and two angles are equal
B. All three corresponding sides are equal
C. Two sides are equal
D. One angle is equal
Answer:B
Explanation: The Side-Side-Side (SSS) criterion states that if all three corresponding sides of two triangles are equal, the triangles must be congruent. Once every side matches, the overall shape and size of the triangles become identical.
Q. In the SAS congruence criterion, which angle must be equal?
A. Any one angle of the triangle
B. The largest angle only
C. The angle included between the two given sides
D. The angle opposite the longest side
Answer:C
Explanation: The SAS rule requires two corresponding sides and the included angle, which is the angle formed between those two sides. If a different angle is considered, the information may not be sufficient to prove that the triangles are congruent.
Q. If ΔABC ≅ ΔPQR, then side AC corresponds to:
A. PQ
B. PR
C. QR
D. QR and PQ
Answer:B
Explanation: In a congruence statement, the order of the vertices is important. Since ΔABC ≅ ΔPQR, the corresponding vertices are A↔P, B↔Q, and C↔R. Therefore, side AC matches side PR. Correctly identifying corresponding parts is essential when applying CPCT and solving geometry problems.
Q. The RHS congruence rule can be applied only to:
A. Equilateral triangles
B. Isosceles triangles
C. Right-angled triangles
D. Scalene triangles
Answer:C
Explanation: The RHS (Right-Hypotenuse-Side) criterion is specifically meant for right-angled triangles. If two right triangles have equal hypotenuses and one corresponding side equal, the triangles are congruent. This rule cannot be applied to triangles that are not right-angled.
Q. Which congruence criterion uses two angles and the side between them?
A. SAS
B. ASA
C. SSS
D. RHS
Answer:B
Explanation: The ASA (Angle-Side-Angle) criterion proves two triangles are congruent when two corresponding angles and the included side are equal. Since the side lies between the given angles, the triangles are uniquely determined and must be identical in shape and size.
Q. If one triangle can be placed exactly over another without any gap, the two triangles are:
A. Similar
B. Congruent
C. Parallel
D. Symmetrical
Answer:B
Explanation: Superposition is a simple way to verify congruence. When one triangle completely covers another after being placed over it, every corresponding side and angle matches perfectly. This confirms that the triangles are congruent.
Q. Which statement is true about congruent triangles?
A. Their corresponding sides are always unequal.
B. Their corresponding angles are equal.
C. Only their areas are equal.
D. Their perimeters must always be different.
Answer:B
Explanation: Congruent triangles have the same shape and size. As a result, all corresponding sides and corresponding angles are equal. Equal area alone does not prove congruence, and congruent triangles also have the same perimeter.
Q. In the congruence statement ΔXYZ ≅ ΔLMN, vertex Y corresponds to:
A. L
B. M
C. N
D. X
Answer:B
Explanation: The order of letters in a congruence statement determines the corresponding vertices. In ΔXYZ ≅ ΔLMN, X↔L, Y↔M, and Z↔N. Reading the statement carefully helps identify matching sides and angles correctly.
Q. Which property allows us to conclude that corresponding sides and angles are equal after proving two triangles congruent?
A. BODMAS
B. Pythagoras Theorem
C. CPCT
D. Midpoint Theorem
Answer:C
Explanation: CPCT stands for Corresponding Parts of Congruent Triangles. After establishing congruence using a valid criterion, CPCT allows us to conclude that all remaining corresponding sides and angles are equal without measuring them separately.
Q. Two triangles have side lengths 4 cm, 6 cm, and 8 cm each. Which congruence rule proves they are geometric twins?
A. ASA
B. SAS
C. SSS
D. RHS
Answer:C
Explanation: Since all three corresponding sides of the triangles are equal, the SSS criterion applies directly. No angle information is required because three matching sides uniquely determine the shape and size of a triangle.
Q. Which of the following does not affect the congruence of a figure?
A. Increasing its size
B. Rotating the figure
C. Stretching one side
D. Changing its dimensions
Answer:B
Explanation: Rotation changes only the orientation of a figure, not its measurements. Therefore, a rotated figure remains congruent to the original. However, enlarging, stretching, or changing dimensions alters the size or shape and destroys congruence.
Q. Why is the order of vertices important in a congruence statement?
A. It determines the colour of the figure.
B. It identifies the corresponding parts correctly.
C. It changes the area of the triangle.
D. It decides whether the triangle is acute or obtuse.
Answer:B
Explanation: The sequence of vertices tells us exactly which sides and angles correspond between two congruent triangles. A correct correspondence is essential while applying congruence rules and using CPCT to solve geometry problems accurately.
Q. Which statement best describes congruent figures?
A. They always have equal areas but may differ in shape.
B. They have the same shape and exactly the same size.
C. They always have equal perimeters only.
D. They contain the same number of angles regardless of size.
Answer:B
Explanation: Congruent figures are identical in every measurement. Their corresponding sides and angles are equal, allowing one figure to fit perfectly over the other through translation, rotation, or reflection. This complete match of shape and size defines congruence.
Q. Two triangles have two equal sides and the included angle equal. Which congruence criterion should be used?
A. ASA
B. RHS
C. SAS
D. SSS
Answer:C
Explanation: The SAS (Side-Angle-Side) criterion applies when two corresponding sides and the angle between them are equal. The included angle is important because it fixes the position of the two sides, ensuring the triangles are identical in both shape and size.
Q. If two triangles are congruent, what can you say about their corresponding angles?
A. They are always supplementary.
B. They are equal.
C. They add up to 90°.
D. They are always different.
Answer:B
Explanation: Congruent triangles have exactly the same shape and size. Therefore, every corresponding angle has the same measure. This property helps students solve unknown angles after proving congruence using one of the valid congruence criteria.
Q. Which of the following is an example of congruent objects?
A. Two circles with different radii
B. Two squares with equal side lengths
C. Two rectangles having the same area but different dimensions
D. Two triangles with equal angles only
Answer:B
Explanation: Squares are congruent only when their corresponding sides are equal. Equal area or equal angles alone cannot guarantee congruence because the actual dimensions of the figures may still be different.
Q. What is the main purpose of using triangle congruence criteria?
A. To calculate the perimeter only
B. To prove two triangles are exactly identical without measuring every part
C. To find the colour of a triangle
D. To determine whether a triangle is equilateral
Answer:B
Explanation: Congruence criteria simplify geometric proofs by allowing us to establish that two triangles are identical using only specific measurements. Once congruence is proved, the remaining corresponding parts can be concluded using CPCT.
Q. In ΔPQR ≅ ΔXYZ, which side corresponds to QR?
A. XY
B. YZ
C. XZ
D. ZX and XY
Answer:B
Explanation: The order of the vertices indicates the correspondence: P↔X, Q↔Y, and R↔Z. Therefore, side QR matches side YZ. Paying attention to the order of letters helps avoid mistakes while applying congruence properties.
Q. Which transformation changes only the position of a figure without changing its shape or size?
A. Stretching
B. Translation
C. Enlargement
D. Compression
Answer:B
Explanation: Translation slides a figure from one position to another while keeping every side length and angle unchanged. Since neither the shape nor the size changes, the translated figure remains congruent to the original.
Q. Why is the AAA condition not considered a triangle congruence criterion?
A. It changes the angles of the triangle.
B. It only proves the triangles are similar, not necessarily equal in size.
C. It is applicable only to right triangles.
D. It requires all sides to be measured.
Answer:B
Explanation: Equal corresponding angles ensure that triangles have the same shape, but their side lengths can still differ. Therefore, AAA establishes similarity rather than congruence. Congruent triangles must match in both shape and size.
Q. After proving two triangles congruent, which theorem helps determine the equality of remaining corresponding parts?
A. Midpoint Theorem
B. Angle Sum Property
C. CPCT
D. Exterior Angle Property
Answer:C
Explanation: CPCT stands for Corresponding Parts of Congruent Triangles. Once congruence is established through a valid criterion, CPCT allows us to conclude that all remaining matching sides and angles are equal without additional proof.
Q. Which statement correctly describes congruent rectangles?
A. They have equal areas only.
B. Their diagonals are equal only.
C. Their corresponding lengths and breadths are equal.
D. They have the same perimeter only.
Answer:C
Explanation: For rectangles to be congruent, both the corresponding lengths and breadths must match. Equal area, equal perimeter, or equal diagonals alone do not ensure that two rectangles are identical in shape and size.
Q. Which statement best summarizes the concept of geometric twins?
A. Figures with equal perimeters are always geometric twins.
B. Figures having the same number of sides are geometric twins.
C. Figures that completely coincide on superposition are called geometric twins.
D. Figures with equal angles are always geometric twins.
Answer:C
Explanation: The idea of superposition is central to understanding geometric twins. If one figure can be placed exactly over another so that every corresponding side and angle matches perfectly, the figures are congruent. This complete overlap confirms that they are geometric twins.
Chapter 9 One-Minute Revision Notes
These quick revision notes will help you recall the most important concepts of the chapter in just a few minutes before your examination.
Important Definitions
Geometry: Geometry is the branch of mathematics that deals with shapes, sizes, positions, and properties of figures.
Point: A point represents an exact location and has no length, breadth, or thickness.
Line: A line extends endlessly in both directions without any endpoints.
Line Segment: A line segment has two fixed endpoints and a measurable length.
Ray: A ray starts from one endpoint and extends infinitely in one direction.
Angle: An angle is formed when two rays meet at a common endpoint called the vertex.
Important Geometric Terms
- Point
- Line
- Line Segment
- Ray
- Vertex
- Angle
- Plane
- Intersecting Lines
- Parallel Lines
- Perpendicular Lines
- Geometric Figures
Types of Lines
Parallel Lines: Lines that never meet, even when extended infinitely.
Intersecting Lines: Lines that cross each other at a point.
Perpendicular Lines: Intersecting lines that meet at an angle of 90°.
Types of Angles
- Acute Angle – Less than 90°
- Right Angle – Exactly 90°
- Obtuse Angle – More than 90° but less than 180°
- Straight Angle – Exactly 180°
- Reflex Angle – More than 180° but less than 360°
- Complete Angle – Exactly 360°
Important Rules
- Every line segment has two endpoints.
- A ray has one endpoint and extends infinitely in one direction.
- A line has no endpoints.
- Two parallel lines never intersect.
- Perpendicular lines always form a right angle.
- Angles are measured in degrees (°).
Important Terms to Remember
- Point
- Line
- Ray
- Line Segment
- Angle
- Vertex
- Parallel Lines
- Perpendicular Lines
- Intersecting Lines
- Geometry
- Plane Figures
- Right Angle
- Acute Angle
- Obtuse Angle
Quick Exam Revision Tips
- Learn the definitions of all basic geometric terms.
- Understand the difference between a line, ray, and line segment.
- Practice identifying different types of angles.
- Revise the properties of parallel and perpendicular lines.
- Draw neat figures while solving geometry-based questions.
- Read every MCQ carefully before selecting the correct option.
- Eliminate incorrect options to improve accuracy.
- Revise the chapter once again before your examination.
