Important Questions Class 8 Maths Chapter 4: Quadrilaterals with Answers

Important Questions Class 8 Maths Chapter 4 focus on quadrilaterals, closed four-sided figures with four angles and four sides. Students use angle sum, diagonal properties, and side relations to solve rectangle, square, parallelogram, rhombus, kite, and trapezium questions.

Quadrilaterals form a major geometry area in Class 8 Maths because they connect angles, sides, diagonals, and proofs. Important Questions Class 8 Maths Chapter 4 help students practise NCERT-style reasoning for rectangles, squares, parallelograms, rhombuses, kites, and trapeziums. The CBSE 2026 pattern can test direct definitions, angle calculations, construction logic, and property-based proofs from this chapter.

Key Takeaways

• Angle Sum: Every quadrilateral has four angles whose sum equals 360°.
• Rectangle Rule: A rectangle has four right angles and equal diagonals that bisect each other.
• Square Rule: A square has equal sides, right angles, and diagonals that meet at 90°.
• Parallelogram Rule: A parallelogram has opposite sides parallel and diagonals that bisect each other.

Important Questions Class 8 Maths Chapter 4 Structure 2026

Important Questions Class 8 Maths Chapter 4 with Answers

Quadrilaterals questions need exact property recall and clear geometric reasoning. These class 8 maths chapter 4 important questions follow the NCERT pattern for Chapter 4.

1. Why does a quadrilateral with three right angles have the fourth angle equal to 90°?

A quadrilateral with three right angles has the fourth angle equal to 90°. The sum of all angles in any quadrilateral is 360°.

1. Given Data: Three angles are 90°, 90°, and 90°.
2. Formula Used: Sum of angles in a quadrilateral = 360°.
3. Calculation:
   Fourth angle = 360° − (90° + 90° + 90°)
   Fourth angle = 360° − 270°
   Fourth angle = 90°.
4. Final Result: The fourth angle is 90°.

2. How do you find the fourth angle when three angles of a quadrilateral are known?

The fourth angle equals 360° minus the sum of the other three angles. This rule applies to every quadrilateral.

1. Given Data: Three angles are 80°, 95°, and 110°.
2. Formula Used: Fourth angle = 360° − sum of three given angles.
3. Calculation:
   Fourth angle = 360° − (80° + 95° + 110°)
   Fourth angle = 360° − 285°
   Fourth angle = 75°.
4. Final Result: The fourth angle is 75°.

3. Why is the sum of angles in a quadrilateral equal to 360°?

The sum of angles in a quadrilateral is 360°. A diagonal divides a quadrilateral into two triangles.

1. Given Data: A quadrilateral ABCD has diagonal AC.
2. Formula Used: Sum of angles in one triangle = 180°.
3. Calculation:
   Triangle ABC has angle sum 180°.
   Triangle ADC has angle sum 180°.
   Total angle sum = 180° + 180° = 360°.
4. Final Result: The angle sum of a quadrilateral is 360°.

Class 8 Maths Chapter 4 Quadrilaterals Extra Questions

Students often confuse quadrilateral families because many shapes share properties. These class 8 maths chapter 4 extra questions separate each shape by its exact NCERT rule.

4. How do you prove that the diagonals of a rectangle are equal?

The diagonals of a rectangle are equal in length. The proof uses congruence between two triangles formed inside the rectangle.

1. Given Data: ABCD is a rectangle.
2. Formula Used: SAS congruence rule.
3. Proof:
   AB = CD because opposite sides of a rectangle are equal.
   ∠BAD = ∠CDA = 90°.
   AD is common to both triangles.
4. Conclusion: ∆ADC ≅ ∆DAB by SAS.
5. Final Result: AC = BD.

5. Why do the diagonals of a rectangle bisect each other?

The diagonals of a rectangle bisect each other. Their point of intersection divides both diagonals into two equal parts.

1. Given Data: Diagonals AC and BD meet at O in rectangle ABCD.
2. Formula Used: AAS congruence rule.
3. Proof:
   Vertically opposite angles at O are equal.
   Corresponding right-angle-based parts form congruent triangles.
   ∆AOB ≅ ∆COD by AAS.
4. Final Result: OA = OC and OB = OD.

6. Can a quadrilateral with all angles equal to 90° be anything other than a rectangle?

No, a quadrilateral with all angles equal to 90° is a rectangle. Opposite sides become equal through triangle congruence.

1. Given Data: ABCD has four right angles.
2. Formula Used: AAS congruence rule.
3. Proof:
   Draw diagonal BD.
   ∆BAD and ∆DCB share side BD.
   Angle relations make the two triangles congruent.
4. Final Result: ABCD is a rectangle.

7. Why is every square also a rectangle?

Every square is a rectangle because it has four angles of 90°. A square adds one extra condition of four equal sides.

1. Given Data: A square has four right angles and four equal sides.
2. Rectangle Rule: A rectangle has four right angles.
3. Comparison:
   A square satisfies the rectangle angle rule.
   A rectangle may not have four equal sides.
4. Final Result: Every square is a rectangle.

8. How do you construct a square when its diagonal is 6 cm?

A square with diagonal 6 cm can be constructed using a perpendicular bisector. The diagonals of a square are equal and meet at 90°.

1. Draw AC = 6 cm.
2. Draw the perpendicular bisector of AC.
3. Mark O as the midpoint of AC.
4. Mark B and D on the perpendicular bisector.
5. Keep OB = OD = 3 cm.
6. Join AB, BC, CD, and DA.
7. Final Result: ABCD is a square with diagonal 6 cm.

Class 8 Maths Quadrilaterals Questions with Answers on Parallelograms

Parallelograms use parallel sides, equal opposite angles, and diagonal bisection. These class 8 maths quadrilaterals questions with answers focus on Chapter 4 proof patterns.

9. How do you find all angles of a parallelogram when one angle is 30°?

The opposite angle is 30°, and each adjacent angle is 150°. Adjacent angles in a parallelogram add to 180°.

1. Given Data: ∠A = 30° in parallelogram ABCD.
2. Formula Used: Adjacent angles = 180°.
3. Calculation:
   ∠B = 180° − 30° = 150°.
   ∠C = ∠A = 30°.
   ∠D = ∠B = 150°.
4. Final Result: Angles are 30°, 150°, 30°, and 150°.

10. How do you prove that opposite sides of a parallelogram are equal?

Opposite sides of a parallelogram are equal. The proof uses congruent triangles formed by a diagonal.

1. Given Data: ABCD is a parallelogram.
2. Formula Used: AAS congruence rule.
3. Proof:
   Draw diagonal BD.
   Alternate angles are equal because opposite sides are parallel.
   BD is common to both triangles.
4. Conclusion: ∆ABD ≅ ∆CDB by AAS.
5. Final Result: AB = CD and AD = BC.

11. How do you prove that diagonals of a parallelogram bisect each other?

The diagonals of a parallelogram bisect each other. Each diagonal gets divided into two equal parts at their intersection point.

1. Given Data: Diagonals of parallelogram EASY meet at O.
2. Formula Used: ASA congruence rule.
3. Proof:
   AE = YS because opposite sides are equal.
   Alternate angles are equal due to parallel sides.
   ∆AOE ≅ ∆YOS by ASA.
4. Final Result: OA = OY and OE = OS.

12. Are the diagonals of a parallelogram always equal?

The diagonals of a parallelogram are not always equal. They are equal only in special cases like rectangles and squares.

1. Given Data: ABCD is a parallelogram.
2. Property Used: Diagonals of a parallelogram bisect each other.
3. Fact:
   A slant parallelogram can have unequal diagonals.
   A rectangle has equal diagonals.
   A square has equal diagonals.
4. Final Result: A parallelogram’s diagonals need not be equal.

NCERT Class 8 Maths Chapter 4 Questions on Rhombus, Kite, and Trapezium

A rhombus, kite, and trapezium need careful side and diagonal checks. These NCERT class 8 maths chapter 4 questions follow the exact chapter sequence.

13. How do you find the angles of a rhombus when one angle is 50°?

The opposite angle is 50°, and each adjacent angle is 130°. A rhombus is also a parallelogram.

1. Given Data: One angle of rhombus ABCD is 50°.
2. Formula Used: Adjacent angles in a parallelogram = 180°.
3. Calculation:
   Adjacent angle = 180° − 50° = 130°.
   Opposite angles are equal.
4. Final Result: The angles are 50°, 130°, 50°, and 130°.

14. Why do the diagonals of a rhombus meet at 90°?

The diagonals of a rhombus meet at 90°. Congruent triangles around the intersection point prove this property.

1. Given Data: GAME is a rhombus, and diagonals meet at O.
2. Formula Used: Rhombus diagonal property.
3. Proof:
   ∆GEO ≅ ∆MEO.
   ∠GOE = ∠MOE as corresponding angles.
   These two angles form a straight angle of 180°.
4. Calculation:
   ∠GOE = ∠MOE = 180° ÷ 2 = 90°.
5. Final Result: The diagonals meet at 90°.

15. Why do the diagonals of a rhombus bisect its angles?

The diagonals of a rhombus bisect its angles. Each diagonal divides opposite angles into two equal parts.

1. Given Data: ABCD is a rhombus.
2. Formula Used: Congruence in equal-sided triangles.
3. Proof:
   All sides of a rhombus are equal.
   A diagonal creates two congruent triangles.
   Corresponding angles become equal.
4. Final Result: Each diagonal bisects a pair of opposite angles.

16. What are the main diagonal properties of a kite?

A kite has one diagonal that bisects the other diagonal at 90°. That same diagonal also bisects two opposite angles.

1. Given Data: In kite ABCD, AB = BC and CD = DA.
2. Property Used: Kite diagonal property.
3. Fact:
   BD bisects ∠ABC and ∠ADC.
   BD bisects AC at O.
   BD is perpendicular to AC.
4. Final Result: BD is the symmetry diagonal of the kite.

17. How do you find the missing angles in a trapezium?

Missing angles in a trapezium use the 180° rule along each non-parallel side. A trapezium has at least one pair of parallel opposite sides.

1. Given Data: PQRS is a trapezium with PQ ∥ SR.
2. Formula Used: Interior angles on the same side of a transversal = 180°.
3. Calculation:
   ∠P + ∠S = 180°.
   ∠Q + ∠R = 180°.
4. Final Result: Each missing angle equals 180° minus its adjacent known angle.

18. Why are base angles equal in an isosceles trapezium?

Base angles in an isosceles trapezium are equal. The equal non-parallel sides create congruent right triangles.

1. Given Data: UV ∥ XW and UX = VW.
2. Formula Used: Congruent triangle property.
3. Proof:
   Draw perpendiculars XY and WZ to UV.
   XWZY forms a rectangle.
   ∆UXY ≅ ∆VWZ.
4. Final Result: ∠U = ∠V.

Class 8 Maths Chapter 4 Solutions for Mixed Practice

Mixed questions train students to identify the quadrilateral before applying any rule. These class 8 maths chapter 4 solutions cover proof, construction, and property-based reasoning.

19. What figure forms when equal perpendicular diameters of a circle are joined?

A square forms when endpoints of equal perpendicular diameters are joined. The diameters act as equal diagonals that bisect each other at 90°.

1. Given Data: PL and AM are perpendicular diameters of a circle with centre O.
2. Formula Used: Square diagonal property.
3. Reason:
   PL = AM because both are diameters of the same circle.
   They bisect each other at O.
   They meet at 90°.
4. Final Result: APML is a square.

20. Can opposite sides parallel and equal define a rectangle?

No, opposite sides parallel and equal define a parallelogram. A rectangle must also have four right angles.

1. Given Data: A quadrilateral has opposite sides parallel and equal.
2. Formula Used: Definition of parallelogram.
3. Reason:
   A parallelogram can have angles of 60° and 120°.
   A rectangle must have four angles of 90°.
4. Final Result: The quadrilateral is a parallelogram, not always a rectangle.

21. If a quadrilateral has four equal sides and one angle of 90°, is it a square?

Yes, the quadrilateral is a square. Four equal sides make it a rhombus, and one right angle makes all angles right angles.

1. Given Data: Four sides are equal, and one angle is 90°.
2. Formula Used: Adjacent angles in a rhombus add to 180°.
3. Calculation:
   Adjacent angle = 180° − 90° = 90°.
   Opposite angles are equal.
4. Final Result: The quadrilateral is a square.

22. What quadrilateral has both pairs of opposite sides equal?

A quadrilateral with both pairs of opposite sides equal is a parallelogram. This result follows from triangle congruence.

1. Given Data: In ABCD, AB = CD and AD = BC.
2. Formula Used: SSS congruence rule.
3. Proof:
   Draw diagonal AC.
   ∆ABC and ∆CDA have three equal side pairs.
   ∆ABC ≅ ∆CDA by SSS.
4. Final Result: ABCD is a parallelogram.

23. Is a quadrilateral with equal diagonals that bisect each other always a square?

No, it is always a rectangle, but not always a square. A square also needs four equal sides or perpendicular diagonals.

1. Given Data: Diagonals are equal and bisect each other.
2. Property Used: Rectangle diagonal property.
3. Fact:
   A rectangle has equal diagonals that bisect each other.
   A square has equal diagonals that meet at 90°.
4. Final Result: The quadrilateral is a rectangle, not necessarily a square.

24. Is a quadrilateral with perpendicular diagonals always a rhombus?

No, perpendicular diagonals alone do not always form a rhombus. A kite can also have perpendicular diagonals.

1. Given Data: Diagonals of a quadrilateral meet at 90°.
2. Property Used: Rhombus and kite diagonal comparison.
3. Fact:
   A rhombus has perpendicular bisecting diagonals.
   A kite has one diagonal perpendicular to the other.
4. Final Result: Perpendicular diagonals alone do not prove a rhombus.

25. What type of quadrilateral is formed by joining two equilateral triangles of side 4 cm?

A rhombus forms when two equilateral triangles of side 4 cm are joined along one side. All outer sides measure 4 cm.

1. Given Data: Two equilateral triangles have side 4 cm.
2. Property Used: Definition of rhombus.
3. Reason:
   Each outer side equals 4 cm.
   The joined side stays inside the figure.
   The outer quadrilateral has four equal sides.
4. Final Result: The quadrilateral is a rhombus.

Class 8 Maths Important Questions Quadrilaterals for Short Answers

Short-answer questions often test one exact rule in one or two marks. These class 8 maths important questions quadrilaterals cover definitions and property matches.

26. What is the difference between a rectangle and a square?

A square has all rectangle properties and four equal sides. A rectangle needs four right angles but does not need four equal sides.

1. Rectangle: Four angles equal 90°.
2. Square: Four angles equal 90° and all sides are equal.
3. Example: A 6 cm by 4 cm shape is a rectangle.
4. Final Result: Every square is a rectangle, but every rectangle is not a square.

27. What is the difference between a rhombus and a square?

A square is a rhombus with four right angles. A rhombus only needs all four sides equal.

1. Rhombus: All sides are equal.
2. Square: All sides are equal and all angles are 90°.
3. Example: A rhombus can have angles 60° and 120°.
4. Final Result: Every square is a rhombus, but every rhombus is not a square.

28. What is the difference between a parallelogram and a trapezium?

A parallelogram has two pairs of parallel opposite sides. A trapezium has at least one pair of parallel opposite sides.

1. Parallelogram: Both pairs of opposite sides are parallel.
2. Trapezium: At least one pair of opposite sides is parallel.
3. Example: A rectangle is a parallelogram.
4. Final Result: Every parallelogram fits the trapezium condition used in Chapter 4.

29. What is the difference between a kite and a rhombus?

A kite has two pairs of equal adjacent sides. A rhombus has all four sides equal.

1. Kite: AB = BC and CD = DA.
2. Rhombus: AB = BC = CD = DA.
3. Example: A rhombus can be treated as a special kite only when side conditions match.
4. Final Result: Every kite is not a rhombus.

30. How are rectangle, square, rhombus, and parallelogram related?

A square belongs to both the rectangle and rhombus groups. Rectangles and rhombuses both belong to the parallelogram group.

1. Rectangle: A parallelogram with four right angles.
2. Rhombus: A parallelogram with four equal sides.
3. Square: A rectangle and a rhombus.
4. Final Result: A square is both a rectangle and a rhombus.

Class 8 Maths Important Questions Chapter-Wise