Important Questions Class 7 Maths Part 2 Chapter 1: Geometric Twins

Important Questions Class 7 Maths Part 2 Chapter 1 focus on congruence, where two figures have the same shape and size.
Students use triangle congruence rules such as SSS, SAS, ASA, AAS, and RHS to prove equal sides, equal angles, and geometric properties.

Congruence gives geometry an exact way to compare figures beyond visual similarity. Important Questions Class 7 Maths Part 2 Chapter 1 help students practise congruent figures, triangle congruence conditions, corresponding parts, and equal angles in isosceles and equilateral triangles. The CBSE 2026 chapter uses replicas, triangular frames, rectangles, kites, right triangles, and real-life structures to show how measurements prove exact sameness.

Key Takeaways

• Congruent Figures: Congruent figures have the same shape and same size.
• SSS Rule: Three equal corresponding sides guarantee triangle congruence.
• SSA Warning: Two sides and a non-included angle do not always guarantee congruence.
• Equilateral Triangle: Every angle of an equilateral triangle measures 60°.

Important Questions Class 7 Maths Part 2 Chapter 1 Structure 2026

Important Questions Class 7 Maths Part 2 Chapter 1 with Answers

Congruence questions ask students to prove exact sameness using measurements.
Students must identify corresponding sides and angles before writing any congruence statement.
These class 7 maths part 2 chapter 1 important questions follow the NCERT 2026 approach for Geometric Twins.

1. What does Important Questions Class 7 Maths Part 2 Chapter 1 test in Geometric Twins?

Important Questions Class 7 Maths Part 2 Chapter 1 test congruent figures, congruent triangles, and triangle congruence rules. The chapter also tests equal angles in isosceles and equilateral triangles.

1. Figure Skill: Check whether two figures have the same shape and size.
2. Triangle Skill: Apply SSS, SAS, ASA, AAS, or RHS.
3. Proof Skill: Match corresponding vertices, sides, and angles.
4. Final Result: The chapter tests exact comparison through congruence.

2. What are congruent figures in Class 7 Maths?

Congruent figures are figures with the same shape and same size. One figure can fit exactly over the other after rotation or flipping.

1. Condition 1: Both figures must have the same shape.
2. Condition 2: Both figures must have the same size.
3. Superimposition Test: One figure must cover the other exactly.
4. Final Result: Congruent figures are exact copies of each other.

3. Why are only two arm lengths not enough to recreate the signboard symbol?

Two arm lengths are not enough because the angle between them can change. The same arm lengths can create different shapes.

1. Given Data: AB = 4 cm and BC = 8 cm.
2. Missing Data: ∠ABC is not given.
3. Reason: Different values of ∠ABC create different symbols.
4. Final Result: AB, BC, and ∠ABC are needed for the exact replica.

Class 7 Maths Part 2 Chapter 1 Geometric Twins

The chapter starts with the idea of recreating a figure exactly.
Students learn that visual matching is not enough when measurements differ.
This class 7 maths part 2 chapter 1 geometric twins section builds the base for triangle congruence.

4. How can you check whether two circles are congruent?

Two circles are congruent if they have the same radius. Equal radii give circles of the same size.

1. Measurement Needed: Radius or diameter.
2. Condition: Radius of circle 1 = Radius of circle 2.
3. Example: Two circles of radius 5 cm are congruent.
4. Final Result: Equal radii prove circle congruence.

5. How can you check whether two rectangles are congruent?

Two rectangles are congruent if their corresponding length and breadth are equal. They may be rotated before comparison.

1. Measurement 1: Length of both rectangles.
2. Measurement 2: Breadth of both rectangles.
3. Condition: Lengths match and breadths match.
4. Final Result: Equal corresponding length and breadth prove rectangle congruence.

6. Can two figures be congruent after flipping?

Yes, two figures can be congruent after flipping. Congruence allows rotation and flipping before superimposition.

1. Given Data: Two figures have the same shape and size.
2. Action: Flip or rotate one figure.
3. Test: Place it over the other figure.
4. Final Result: Flipping does not change congruence.

Congruent Figures Class 7 Questions

Congruent figures need exact overlap, not approximate similarity.
The chapter uses tracing, cutouts, and measurement checks to explain superimposition.
These congruent figures class 7 questions focus on shape, size, rotation, and corresponding parts.

7. What measurements create a figure congruent to an angle-shaped symbol?

The two arm lengths and the included angle create a congruent angle-shaped symbol. These three measurements fix shape and size.

1. Given Data: AB = 4 cm, BC = 8 cm, and ∠ABC = 80°.
2. Construction Step: Draw BC = 8 cm.
3. Angle Step: Construct ∠ABC = 80° at B.
4. Length Step: Mark A on the new arm with AB = 4 cm.
5. Final Result: The new symbol is congruent to the original symbol.

8. Why do figures with the same shape but different size fail congruence?

Figures with the same shape but different size fail congruence because congruence needs exact size. Such figures cannot overlap exactly.

1. Given Data: Two figures look similar.
2. Problem: Their side lengths differ.
3. Superimposition Test: One figure does not cover the other exactly.
4. Final Result: Same shape alone does not prove congruence.

9. What are corresponding parts in congruent figures?

Corresponding parts are the matching sides, angles, or vertices that overlap exactly. They must be written in the correct order.

1. Example: In ∆ABC ≅ ∆XYZ, A corresponds to X.
2. Side Match: AB corresponds to XY.
3. Angle Match: ∠B corresponds to ∠Y.
4. Final Result: Corresponding parts show exact matching in congruent figures.

Congruence of Triangles Class 7 Questions

Triangle congruence uses limited measurements to prove exact equality.
The chapter checks which combinations are enough and which combinations fail.
These congruence of triangles class 7 questions cover SSS, SAS, ASA, AAS, RHS, and SSA.

10. What does ∆ABC ≅ ∆XYZ mean?

∆ABC ≅ ∆XYZ means the two triangles are congruent with matching vertex order. A corresponds to X, B corresponds to Y, and C corresponds to Z.

1. Vertex Match: A ↔ X, B ↔ Y, C ↔ Z.
2. Side Match: AB ↔ XY, BC ↔ YZ, AC ↔ XZ.
3. Angle Match: ∠A ↔ ∠X, ∠B ↔ ∠Y, ∠C ↔ ∠Z.
4. Final Result: The order shows the corresponding parts.

11. Why is ∆ACB ≅ ∆XYZ incorrect when ∆ABC ≅ ∆XYZ?

∆ACB ≅ ∆XYZ is incorrect because the vertex order changes the corresponding parts. It matches C with Y instead of B with Y.

1. Correct Order: ∆ABC ≅ ∆XYZ.
2. Correct Match: B corresponds to Y.
3. Wrong Order: ∆ACB matches C to Y.
4. Final Result: Congruence statements must preserve corresponding vertices.

12. How do you list corresponding sides when ∆HEN ≅ ∆BIG?

The corresponding sides are HE ↔ BI, EN ↔ IG, and HN ↔ BG. The order of letters gives the match.

1. Given Data: ∆HEN ≅ ∆BIG.
2. Vertex Match: H ↔ B, E ↔ I, N ↔ G.
3. Side Match: HE ↔ BI, EN ↔ IG, HN ↔ BG.
4. Final Result: Corresponding sides follow the triangle name order.

SSS Congruence Class 7 Questions

SSS uses three pairs of equal sides to prove triangle congruence.
It is useful when all side lengths are given or shared by a common side.
These SSS congruence class 7 questions follow the cardboard triangle and rectangle examples.

13. What is the SSS condition for triangle congruence?

The SSS condition says two triangles are congruent when their three corresponding sides are equal. SSS means Side Side Side.

1. Condition: Three sides of one triangle equal three sides of another triangle.
2. Example: 4 cm, 6 cm, and 8 cm match 4 cm, 6 cm, and 8 cm.
3. Result: Only congruent triangles can be formed.
4. Final Result: SSS guarantees triangle congruence.

14. Why are triangles with sides 4 cm, 6 cm, and 8 cm congruent?

Triangles with sides 4 cm, 6 cm, and 8 cm are congruent by SSS. Their three corresponding sides are equal.

1. Given Data: Side lengths are 4 cm, 6 cm, and 8 cm.
2. Congruence Rule: SSS.
3. Reason: All three sides match in both triangles.
4. Final Result: The triangles are congruent by SSS.

15. Why are ∆ABD and ∆CDB congruent in rectangle ABCD?

∆ABD and ∆CDB are congruent by SSS. Opposite sides of a rectangle are equal, and BD is common.

1. Given Data: ABCD is a rectangle.
2. Equal Sides: AB = CD and AD = CB.
3. Common Side: BD = BD.
4. Congruence Rule: SSS.
5. Final Result: ∆ABD ≅ ∆CDB by SSS.

SAS Congruence Class 7 Questions

SAS uses two sides and the included angle between them.
The included angle matters because a non-included angle can create two different triangles.
These SAS congruence class 7 questions show why the angle position decides congruence.

16. What is the SAS condition for congruence?

The SAS condition says two triangles are congruent when two sides and the included angle are equal. SAS means Side Angle Side.

1. Side Pair 1: One side pair must match.
2. Included Angle: The angle between the two sides must match.
3. Side Pair 2: The second side pair must match.
4. Final Result: SAS guarantees congruence when the angle is included.

17. Are two triangles congruent if AB = XY, AC = XZ, and ∠A = ∠X?

Yes, the triangles are congruent if the equal angle lies between the equal sides. This is the SAS condition.

1. Given Data: AB = XY and AC = XZ.
2. Included Angles: ∠A = ∠X.
3. Congruence Rule: SAS.
4. Final Result: ∆ABC ≅ ∆XYZ by SAS.

18. Why does SSA not always guarantee congruence?

SSA does not always guarantee congruence because two different triangles can satisfy the same measurements. The angle is not included between the two given sides.

1. Given Data: Two sides and a non-included angle.
2. Construction Result: The arc can meet the angle arm at two points.
3. Problem: Two non-congruent triangles can form.
4. Final Result: SSA does not always prove congruence.

ASA Congruence Class 7 Questions

ASA uses two angles and the side included between them.
The included side fixes the triangle’s size, while the two angles fix its shape.
These ASA congruence class 7 questions use exact angle-side-angle matching.

19. What is the ASA condition for congruence?

The ASA condition says two triangles are congruent when two angles and their included side are equal. ASA means Angle Side Angle.

1. Angle Pair 1: One angle pair must match.
2. Included Side: The side between those angles must match.
3. Angle Pair 2: The second angle pair must match.
4. Final Result: ASA guarantees triangle congruence.

20. Are triangles congruent if BC = YZ, ∠B = ∠Y, and ∠C = ∠Z?

Yes, the triangles are congruent by ASA. The equal side lies between the two equal angles.

1. Given Data: BC = YZ.
2. Equal Angles: ∠B = ∠Y and ∠C = ∠Z.
3. Congruence Rule: ASA.
4. Final Result: ∆ABC ≅ ∆XYZ by ASA.

21. Why do three equal angles not prove congruence?

Three equal angles do not prove congruence because triangles can have the same shape but different sizes. Congruence needs same size.

1. Given Data: Angles are 30°, 70°, and 80°.
2. Observation: Many triangles can have these angles.
3. Problem: Their side lengths may differ.
4. Final Result: AAA does not guarantee congruence.

AAS Congruence Class 7 Questions

AAS uses two angles and a non-included side.
The third angle can be found using the angle sum of a triangle.
These AAS congruence class 7 questions show how AAS reduces to ASA.

22. What is the AAS condition for congruence?

The AAS condition says two triangles are congruent when two angles and a non-included side are equal. The third angle becomes fixed.

1. Given Parts: Two angles and one side.
2. Angle Sum Rule: ∠A + ∠B + ∠C = 180°.
3. Reason: The third angle can be calculated.
4. Final Result: AAS guarantees triangle congruence.

23. How do you prove AAS congruence when ∠A = 35°, ∠C = 75°, and BC = 4 cm?

AAS congruence works because the missing angle equals 70°. The triangles then satisfy ASA.

1. Given Data: ∠A = 35°, ∠C = 75°, and BC = 4 cm.
2. Formula Used: Sum of angles of a triangle = 180°.
3. Calculation:
   ∠B = 180° − (35° + 75°)
   ∠B = 180° − 110°
   ∠B = 70°
4. Final Result: The triangles are congruent by AAS.

24. Why does AAS guarantee congruence but AAA does not?

AAS guarantees congruence because it includes one side length. AAA gives only shape and does not fix size.

1. AAS Data: Two angles and one side.
2. AAA Data: Three angles only.
3. Size Check: A side length fixes the triangle size.
4. Final Result: AAS proves congruence, but AAA does not.

RHS Congruence Class 7 Questions

RHS applies only to right-angled triangles.
It uses the right angle, the hypotenuse, and one corresponding side.
These RHS congruence class 7 questions focus on the special right-triangle case.

25. What is the RHS condition for congruence?

The RHS condition says two right triangles are congruent when their hypotenuse and one side are equal. RHS means Right Hypotenuse Side.

1. Condition 1: Both triangles have a right angle.
2. Condition 2: Hypotenuse lengths are equal.
3. Condition 3: One corresponding side is equal.
4. Final Result: RHS guarantees congruence in right triangles.

26. Are right triangles congruent if BC = YZ = 4 cm and AC = XZ = 5 cm?

Yes, the right triangles are congruent by RHS. The hypotenuse and one side are equal.

1. Given Data: ∠B = ∠Y = 90°.
2. Side Pair: BC = YZ = 4 cm.
3. Hypotenuse Pair: AC = XZ = 5 cm.
4. Congruence Rule: RHS.
5. Final Result: ∆ABC ≅ ∆XYZ by RHS.

27. Why is the side opposite the right angle called the hypotenuse?

The side opposite the right angle is called the hypotenuse. It is the longest side of a right-angled triangle.

1. Triangle Type: Right-angled triangle.
2. Right Angle: One angle measures 90°.
3. Opposite Side: The side across the 90° angle is the hypotenuse.
4. Final Result: The hypotenuse lies opposite the right angle.

Class 7 Maths Congruence Questions on Isosceles Triangles

Congruence helps prove properties of isosceles triangles.
When two sides are equal, the angles opposite those sides are also equal.
These class 7 maths congruence questions connect RHS congruence with equal base angles.

28. Why are base angles of an isosceles triangle equal?

Base angles of an isosceles triangle are equal because they are corresponding angles of congruent triangles. An altitude creates two right triangles.

1. Given Data: AB = AC in ∆ABC.
2. Construction: Draw altitude AD to BC.
3. Right Angles: ∠ADB = ∠ADC = 90°.
4. Common Side: AD = AD.
5. Congruence Rule: RHS.
6. Final Result: ∠B = ∠C.

29. If AB = AC and ∠A = 80°, what are ∠B and ∠C?

∠B and ∠C are 50° each. The base angles of an isosceles triangle are equal.

1. Given Data: AB = AC and ∠A = 80°.
2. Formula Used: Sum of triangle angles = 180°.
3. Calculation:
   ∠B + ∠C = 180° − 80° = 100°
   ∠B = ∠C
   ∠B = ∠C = 100° ÷ 2 = 50°
4. Final Result: ∠B = 50° and ∠C = 50°.

Isosceles Triangle Class 7 Questions

Isosceles triangle questions test equal sides and equal opposite angles.
The chapter proves this result using congruent right triangles.
These isosceles triangle class 7 questions focus on angle calculation from side equality.

30. If an isosceles triangle has base angles of 65° each, what is the vertex angle?

The vertex angle is 50°. The three angles of a triangle add to 180°.

1. Given Data: Base angles = 65° and 65°.
2. Formula Used: Vertex angle = 180° − sum of base angles.
3. Calculation:
   Vertex angle = 180° − (65° + 65°)
   Vertex angle = 180° − 130°
   Vertex angle = 50°
4. Final Result: The vertex angle is 50°.

31. If two angles of a triangle are equal, what can you say about the opposite sides?

The opposite sides are equal when two angles of a triangle are equal. This creates an isosceles triangle.

1. Given Data: ∠B = ∠C.
2. Triangle Fact: Equal angles have equal opposite sides.
3. Side Match: AB = AC.
4. Final Result: The triangle is isosceles.

Equilateral Triangle Class 7 Questions

An equilateral triangle has all three sides equal.
Congruence reasoning shows that all three angles also become equal.
These equilateral triangle class 7 questions focus on the 60° angle result.

32. Why is every angle of an equilateral triangle 60°?

Every angle of an equilateral triangle is 60° because all three angles are equal. Their total is 180°.

1. Given Data: AB = BC = CA.
2. Angle Fact: Angles opposite equal sides are equal.
3. Calculation:
   ∠A = ∠B = ∠C
   3 × each angle = 180°
   Each angle = 60°
4. Final Result: Each angle of an equilateral triangle is 60°.

33. Can an equilateral triangle also be called isosceles?

Yes, an equilateral triangle can be called isosceles because it has at least two equal sides. It has three equal sides.

1. Isosceles Condition: At least two equal sides.
2. Equilateral Condition: Three equal sides.
3. Comparison: Three equal sides include two equal sides.
4. Final Result: Every equilateral triangle is also isosceles.

34. What is the angle sum check for an equilateral triangle?

The angle sum check is 60° + 60° + 60° = 180°. It matches the triangle angle sum rule.

1. Given Data: Each angle = 60°.
2. Formula Used: Sum of triangle angles = 180°.
3. Calculation:
   60° + 60° + 60° = 180°
4. Final Result: The angle sum is correct.

NCERT Class 7 Maths Part 2 Chapter 1 Questions for Mixed Practice

Mixed practice questions combine congruence rules with corresponding parts.
Students must first identify the given equal parts before choosing SSS, SAS, ASA, AAS, or RHS.
These NCERT class 7 maths part 2 chapter 1 questions match the proof style in the 2026 chapter.

35. If AB = AD and CB = CD, which triangles are congruent?

∆ABC and ∆ADC are congruent by SSS. They share side AC.

1. Given Data: AB = AD and CB = CD.
2. Common Side: AC = AC.
3. Congruence Rule: SSS.
4. Final Result: ∆ABC ≅ ∆ADC by SSS.

36. Does AC divide ∠BAD and ∠BCD into two equal parts?

Yes, AC divides both angles into two equal parts. Corresponding angles of congruent triangles are equal.

1. Given Data: ∆ABC ≅ ∆ADC.
2. Angle Pair 1: ∠BAC = ∠CAD.
3. Angle Pair 2: ∠BCA = ∠ACD.
4. Final Result: AC bisects ∠BAD and ∠BCD.

37. If O is the midpoint of AD and BC, why is AB = CD?

AB = CD because ∆AOB and ∆DOC are congruent by SAS. The included angles are vertically opposite angles.

1. Given Data: AO = OD and BO = OC.
2. Angle Fact: ∠AOB = ∠DOC.
3. Congruence Rule: SAS.
4. Corresponding Sides: AB ↔ CD.
5. Final Result: AB = CD.

38. If OB = OC and OA = OD, how can you show AB is parallel to CD?

AB is parallel to CD because alternate angles become equal through congruent triangles. The triangles around O satisfy SAS.

1. Given Data: OB = OC and OA = OD.
2. Angle Fact: ∠AOB = ∠COD.
3. Congruence Rule: ∆AOB ≅ ∆DOC by SAS.
4. Equal Angles: ∠BAO = ∠CDO.
5. Final Result: AB ∥ CD.

Class 7 Maths Part 2 Chapter 1 Questions and Answers for One-Mark Practice

One-mark questions usually test exact definitions and rule names.
Students should know congruent figures, corresponding parts, SSS, SAS, ASA, AAS, RHS, and hypotenuse.
These class 7 maths part 2 chapter 1 questions and answers cover the core NCERT terms.

39. What is the full form of SSS in triangle congruence?

SSS stands for Side Side Side. It proves congruence when three corresponding sides are equal.

1. S: Side.
2. S: Side.
3. S: Side.
4. Final Result: SSS means Side Side Side.

40. What is the full form of SAS in triangle congruence?

SAS stands for Side Angle Side. It proves congruence when two sides and the included angle are equal.

1. S: Side.
2. A: Included angle.
3. S: Side.
4. Final Result: SAS means Side Angle Side.

41. What is the full form of RHS in triangle congruence?

RHS stands for Right Hypotenuse Side. It applies only to right-angled triangles.

1. R: Right angle.
2. H: Hypotenuse.
3. S: Side.
4. Final Result: RHS means Right Hypotenuse Side.

42. Which triangle congruence conditions guarantee congruence in Class 7?

SSS, SAS, ASA, AAS, and RHS guarantee congruence in Class 7. SSA does not always guarantee congruence.

1. Valid Conditions: SSS, SAS, ASA, AAS, RHS.
2. Invalid General Case: SSA.
3. Reason: SSA can form two non-congruent triangles.
4. Final Result: Five conditions guarantee congruence.

CBSE Class 7 Maths Important Links