Any2Quiz
Quizzes / CBSE / Class 9 / Mathematics / Quadrilaterals

Quadrilaterals Quiz - CBSE Class 9 Mathematics

Free practice quiz: Quadrilaterals (CBSE Class 9 Mathematics). 15 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

This CBSE Class 9 Mathematics practice quiz has 15 multiple-choice questions on Quadrilaterals, and 15 of them come with an explanation. Try the 5 sample questions below (tap an option to check yourself), then play the full quiz online. No sign-up needed.

Start quiz: 15 questions, free

Learn the key ideas first ↓

Learn the key ideas Beta

Basics of a Quadrilateral

  • A quadrilateral is a closed figure with four sides, four angles, four vertices and two diagonals.
  • A diagonal joins two opposite vertices. It splits the quadrilateral into two triangles.
  • Each triangle has angle sum 180°, so the four angles of any quadrilateral add up to 360°.
Angle sum property
\[\angle A + \angle B + \angle C + \angle D = 360^\circ\]
Finding a missing angle
\[\angle D = 360^\circ - (\angle A + \angle B + \angle C)\]

Common mistake: Using 180° as the angle sum of a quadrilateral. That is the angle sum of a triangle only.

Properties of a Parallelogram

  • A parallelogram has both pairs of opposite sides parallel. Opposite sides are equal and opposite angles are equal.
  • Adjacent angles are supplementary, so they add up to 180°.
  • Its diagonals bisect each other. They need not be equal or perpendicular.
Adjacent angles
\[\angle A + \angle B = 180^\circ\]
Opposite angles
\[\angle A = \angle C,\quad \angle B = \angle D\]
Diagonals AC and BD meet at O
\[OA = OC,\quad OB = OD\]

Common mistake: Assuming the diagonals of every parallelogram are equal or perpendicular. They only bisect each other.

Rectangle, Rhombus and Square

  • A rectangle is a parallelogram with all angles 90°. Its diagonals are equal and bisect each other.
  • A rhombus is a parallelogram with all sides equal. Its diagonals are perpendicular bisectors of each other.
  • A square is both a rectangle and a rhombus. Its diagonals are equal, perpendicular and bisect each other.
Rectangle diagonal (Pythagoras)
\[d = \sqrt{l^2 + b^2}\]
Rhombus side from its diagonals
\[a^2 = \left(\frac{d_1}{2}\right)^2 + \left(\frac{d_2}{2}\right)^2\]
Square diagonal
\[d = a\sqrt{2}\]

Common mistake: Assuming rhombus diagonals are equal. Only rectangle and square diagonals are equal. Rhombus diagonals are perpendicular but usually unequal.

Trapezium and Kite

  • A trapezium has exactly one pair of parallel sides.
  • A kite has two pairs of equal adjacent sides. Its diagonals are perpendicular to each other.
  • In a kite, the pair of opposite angles between the unequal sides is equal.
Area of kite or rhombus
\[\text{Area} = \frac{1}{2} \times d_1 \times d_2\]
Area of trapezium
\[\text{Area} = \frac{1}{2}(a + b) \times h\]

Common mistake: Thinking both pairs of opposite angles in a kite are equal. Only one pair is equal.

Exam tips

Beta: made with AI and checked by a second AI. A teacher has not reviewed it yet.

Sample questions

  1. Which of the following is not a property of a parallelogram?

    Show answer

    Answer: D. All sides are equal

    In a parallelogram, opposite sides are equal, and opposite angles are equal, and the diagonals bisect each other. However, not all sides are equal; that is a characteristic of a rhombus.

  2. What is the sum of the interior angles of a quadrilateral?

    Show answer

    Answer: B. 360 degrees

    The sum of the interior angles of a quadrilateral is always 360 degrees, calculated as (n-2)*180 where n is the number of sides.

  3. What are the properties of the diagonals in a parallelogram?

    Show answer

    Answer: B. They bisect each other

    In a parallelogram, the diagonals bisect each other, which means they divide each other into two equal halves.

  4. Which geometric shape is a quadrilateral with opposite sides that are parallel but does not have equal sides?

    Show answer

    Answer: C. Parallelogram

    A parallelogram has opposite sides that are parallel but not necessarily equal. This differentiates it from a rectangle and square.

  5. In a kite, which of the following is true about one pair of opposite angles?

    Show answer

    Answer: A. They are equal

    In a kite, one pair of opposite angles are equal, typically the angles between the unequal sides.

Take the full quiz

More questions in this quiz

Answers and explanations are in the full quiz.

  1. How many sides does a quadrilateral have?
  2. Which of the following quadrilaterals has only one pair of parallel sides?
  3. If a quadrilateral is classified as a rhombus, what additional property does it have?
  4. Which type of quadrilateral has adjacent sides congruent and diagonals that intersect at right angles?
  5. If a kite has diagonals of lengths 12 cm and 16 cm, what is the area of the kite?
  6. In which quadrilateral are the diagonals always perpendicular to each other and equal in length?
  7. What is the relationship between diagonal lengths in a rectangle?
  8. Which of the following quadrilaterals has both perpendicular bisected diagonals and all equal sides?
  9. A quadrilateral has equal diagonals that bisect each other. What is the shape?
  10. In a rectangle, what is the relationship between the sides and diagonals?

Browse all Quadrilaterals quizzes

More to play

Daily ChallengeA new quiz every day. Keep your streak.HangmanGuess the word, letter by letter.Story QuestLearn through short interactive stories.All quizzesCBSE, ICSE, competitive exams and more.