Geometric Twins - Class 7 Mathematics (CBSE)

Based on the 2026-27 Class 7 Mathematics sequence for NCERT Ganita Prakash. These notes are written for students: understand the idea first, then practise enough examples to become accurate.

1. Why this chapter matters

Two shapes may look like twins when they have the same size and same shape, even if one is turned or flipped. This chapter prepares students for congruence by training them to compare figures through sides, angles, and movement rather than by rough appearance.

In school tests, this chapter can appear as direct calculations, reasoning questions, short explanations, activity-based questions, and word problems. The safest preparation is not to memorise a single trick, but to know what each idea means and when to use it.

2. Core ideas

Same shape and same size

Geometric twins are congruent figures. If one can be moved, turned, or flipped to fit exactly on another, the figures are congruent.

Corresponding parts

Matching sides and matching angles are called corresponding parts. Conguent figures have equal corresponding sides and equal corresponding angles.

Transformations

Sliding, turning, and flipping do not change size or shape. Stretching changes size, so it does not preserve congruence.

3. Rules and formulas to remember

• Congruent symbol: A congruent B. Means figures have same shape and same size.
• Corresponding sides: AB = PQ, BC = QR, CA = RP. Used when triangles match in order.
• Corresponding angles: Angle A = Angle P. Angle matching depends on vertex order.

4. Worked examples

Example 1: Are two circles of radius 5 cm congruent?

Yes. They have the same shape and same size.

Example 2: Are two squares with sides 4 cm and 6 cm congruent?

No. They have the same shape but different sizes.

Example 3: If triangle ABC is congruent to triangle PQR, and AB = 7 cm, what is PQ?

PQ corresponds to AB, so PQ = 7 cm.

Example 4: Does rotating a rectangle make a new non-congruent figure?

No. Rotation preserves size and shape.

5. Activity corner

Trace a triangle on paper, cut it out, and place it over other triangles. If it fits exactly after sliding, rotating, or flipping, the triangles are congruent.

When writing an activity answer, include three things:

• What you did.
• What you observed.
• What mathematical rule or pattern the activity shows.

6. Common mistakes and how to avoid them

• Mistake: Calling similar-looking figures congruent Fix: Congruence needs same size as well as same shape.
• Mistake: Matching wrong vertices Fix: Write the vertex order carefully.
• Mistake: Thinking rotated figures are different Fix: Turning a figure does not change it.

7. How to write high-scoring answers

1. State the given information in mathematical form.
2. Write the rule, formula, diagram, table, or operation you are using.
3. Show every step clearly.
4. Keep units such as cm, m, rupees, degrees, or minutes where needed.
5. Check whether the answer is reasonable.

8. Practice set

1. Are two 3 cm x 5 cm rectangles congruent?
2. Are all circles congruent?
3. If triangle ABC congruent triangle DEF, name the side corresponding to BC.
4. What transformation flips a figure?
5. Does enlargement preserve congruence?
6. Why are corresponding parts important?

9. Answer key

1. Are two 3 cm x 5 cm rectangles congruent? Answer: Yes.

2. Are all circles congruent? Answer: No, only circles with equal radii are congruent.

3. If triangle ABC congruent triangle DEF, name the side corresponding to BC. Answer: EF.

4. What transformation flips a figure? Answer: Reflection.

5. Does enlargement preserve congruence? Answer: No.

6. Why are corresponding parts important? Answer: They tell which measurements must be equal.

10. Quick revision

• Main themes: congruence, symmetry, equal shapes, transformations.
• Redo the worked examples without looking at the solutions.
• Explain the activity in your own words.
• Correct the common mistakes once before the test.
• Create one new word problem from daily life and solve it step by step.