08_Quadrilaterals_Practice Paper

 

Mathematics

Grade-VIII(CBSE)

Quadrilaterals                                  

What is Quadrilateral?

A quadrilateral is a closed polygon with four sides, four angles, and four vertices.

Properties:
The sum of interior angles of a quadrilateral is always 360°.
It has two diagonals.

Types of Quadrilaterals

 

Type	Description	Properties
Parallelogram	Opposite sides are parallel and equal.	Opposite angles are equal, Diagonals bisect each other.
Rectangle	A parallelogram with all angles 90°.	Opposite sides equal, Diagonals equal and bisect each other.
Square	A rectangle with all sides equal.	All angles 90°, All sides equal, Diagonals equal and perpendicular bisectors.
Rhombus	A parallelogram with all sides equal.	Opposite angles equal, Diagonals bisect each other at right angles.
Trapezium	One pair of opposite sides is parallel.	Non-parallel sides called legs.
Kite	Two pairs of adjacent sides are equal.	Diagonals intersect at right angles, one diagonal bisects the other.

Angle Sum Property

The sum of the interior angles of any quadrilateral is always 360⁰
∠A + ∠B + ∠C + ∠D = 360°

Properties of Special Quadrilaterals

 

Quadrilateral	Opp. Sides	Opp. Angles	Diagonals	Angle
Parallelogram	Equal & Parallel	Equal	Bisect each other	Not necessarily 90°
Rectangle	Equal & Parallel	Equal	Equal and bisect	All 90°
Square	Equal & Parallel	Equal	Equal, perpendicular, bisect	All 90°
Rhombus	Equal & Parallel	Equal	Perpendicular and bisect	Not necessarily 90°
Trapezium	One pair parallel	No specific property	No specific property	Varies
Kite	Adjacent sides equal	One pair equal	One bisects the other at 90°	Varies

Important Theorems & Rules

1. Angle Sum Property: Sum of interior angles = 360°.
2. Diagonals of a rectangle are equal and bisect each other.
3. Diagonals of a square are equal and perpendicular bisectors.
4. Diagonals of a rhombus are perpendicular but not necessarily equal.

Practice Questions

Section A: Objective Type Questions

 

Q1. The sum of all interior angles of a quadrilateral is:
   (a)     90°                  (b) 180°                       (c) 270°                                   (d) 360°

Q2. A square is also a:
   (a) Parallelogram     (b) Rhombus               (c) Rectangle                           (d) All of these

Q3. The diagonals of a rhombus:
  (a) Are equal             (b) Bisect at 90°          (c) Do not bisect each other    (d) Are not perpendicular

Section B: Very Short Answer Type

 

Q4. Name the quadrilateral which has only one pair of parallel sides.

Q5. Find the fourth angle of a quadrilateral if three angles are 110°, 85°, and 95°.

Section C: Short Answer Type

Q6. In a parallelogram, if one angle is 70°, find the other three angles.

Q7. A quadrilateral has angles 90°, 80°, and 110°. Find the fourth angle.

Q8. List the properties of a rectangle.

Section D: Long Answer Type

Q9. Prove that the diagonals of a rhombus bisect each other at right angles.

Q10. In a quadrilateral ABCD, ∠A = 75°, ∠B = 85°, ∠C = 110°. Find ∠D. Is the quadrilateral cyclic?

Solutions

Section A Answers:

Q1. (d) 360°
Q2. (d) All of these
Q3. (b) Bisect each other at 90°

Section B Solutions:

Q4. Trapezium

Q5. 360° − (110° + 85° + 95°) = 70°

Section C Solutions:

Q6. One angle = 70°, then others are 110°, 70°, and 110°.

Q7. 360 − (90 + 80 + 110) = 80°

Q8. - Opposite sides equal & parallel
- All angles 90°
- Diagonals equal and bisect each otherSection D Solutions:

Q9. Let ABCD be a rhombus.

Diagonals AC and BD intersect at O.

All sides are equal. (definition of rhombus)

Triangles AOB and COB are congruent (by SSS).

∠AOB = ∠COB, (cpct)

hence diagonals bisect at 90°.

Q10. ∠D = 360 − (75 + 85 + 110) = 90°
Since ∠A + ∠C = 185° ≠ 180°, the quadrilateral is not cyclic.

PDF of this notes is available here-https://t.me/cgscbsesupportbypramodsir/48