Quadrilaterals MCQs – NCERT Mathematics Class IX Ch.8 | Academia Aeternum
NCERT  ·  Mathematics  ·  Class IX  ·  Ch.8

Quadrilaterals
MCQ Master Series

Angle Sum · Parallelogram Family · Mid-point Theorem · Special Quadrilaterals

🎯 50 Questions
⏱ 40 min Suggested
📊 3 Tiers
🗂 5 Topics
⚡ Start Quiz 📊 Analytics
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Question Intelligence

Quiz Analytics

A data-driven breakdown of all 50 questions by difficulty, exam origin and topic distribution.

📈 Distribution Overview

50
Total Questions
Concept Check (NCERT)
34
Boards-Level Reasoning
12
Diagram / HOTS MCQs
4

🗂 Topic Coverage

Angle Sum & Exterior Angles
12%
Parallelogram Properties
32%
Special Quadrilaterals Family
28%
Diagonals & Classification
16%
Mid-point Theorem & Constructions
12%
34
Concept Check (NCERT)
12
Boards-Level Reasoning
4
Diagram / HOTS MCQs
Conceptual Framework

Key Concept Highlights

6 foundational pillars that power every question in this quiz. Understand these, and the answers follow naturally.

⬛
Angle Sum in Quadrilaterals
The sum of interior angles of any quadrilateral is 360°, and this fact combines with properties of parallel lines to relate adjacent and opposite angles in parallelograms.
🟰
Parallelogram Core Properties
In a parallelogram, opposite sides are parallel and equal, opposite angles are equal, adjacent angles are supplementary and the diagonals bisect each other.
📐
Special Parallelograms
Rectangles have right angles and equal diagonals, rhombuses have all sides equal and perpendicular diagonals, while squares satisfy both sets of properties.
🔻
Mid-point Theorem & Mid-Quadrilateral
The line segment joining mid-points of two sides of a triangle is parallel to the third side and half its length; joining mid-points of all sides of a quadrilateral always forms a parallelogram.
🪁
Kite & Trapezium
A kite has two pairs of adjacent equal sides and perpendicular diagonals, while a trapezium (trapezoid) has exactly one pair of opposite sides parallel.
⭕
Cyclic Quadrilaterals
A cyclic quadrilateral has all its vertices on a circle and its opposite angles are supplementary, a key property used to identify or prove cyclic figures.
Pedagogical Value

Why MCQs Matter

Multiple-choice questions are not mere guessing games — they are the sharpest diagnostic tool available to a competitive exam aspirant.

~10–12%
of Class 9 Maths Geometry weightage under “Quadrilaterals” in school exams, periodic tests and final assessments.
Learning Outcomes

What You Will Learn

By completing this quiz set you will have exercised all the following competencies.

01 Use the angle sum property of a quadrilateral and the exterior angle result to quickly find unknown angles in figures.
02 Recall and apply standard properties of parallelograms, rectangles, rhombuses, squares, kites and trapeziums to classify a given quadrilateral.
03 Decide when a quadrilateral is a parallelogram using conditions like equal and parallel opposite sides or diagonals that bisect each other.
04 Use properties of diagonals—equal, perpendicular, bisecting and angle bisectors—to distinguish between rectangle, rhombus, square, kite and general parallelogram.
05 Apply the mid-point theorem to triangles and use the mid-point quadrilateral result to prove figures are parallelograms in coordinate-free geometry questions.
06 Count diagonals from a vertex and in a polygon using simple formulas and reasoning about vertex–vertex joins.
07 Interpret “if–then” descriptions in MCQs, such as “parallelogram with equal diagonals” or “parallelogram with perpendicular diagonals”, and identify the correct special quadrilateral.
Exam Preparation

Strategy & Preparation Tips

5 evidence-based strategies to maximise your score in CBSE Boards and JEE.

Step 01
Group Properties by Family
Make one compact sheet showing parallelogram, rectangle, rhombus, square, kite and trapezium with columns for sides, angles and diagonals; most of your MCQs are direct property picks.
Step 02
Translate Words to Diagrams
For items like “diagonals equal and perpendicular” or “one angle right in a parallelogram”, quickly sketch a rough figure and label, then decide whether it is a rectangle, rhombus or square.
Step 03
Memorise Key “Triggers”
Remember triggers such as “diagonals bisect each other” ⇒ parallelogram, “diagonals equal” ⇒ rectangle or square, “diagonals perpendicular” ⇒ rhombus or kite to eliminate wrong options fast.
Step 04
Use Angle Sum Smartly
For angle-based MCQs, first apply the 360° sum and then the parallelogram relations for opposite and adjacent angles instead of doing random calculations.
Step 05
Practise Mid-point Applications
Solve a few proofs and MCQs where the mid-point theorem and the mid-point quadrilateral are used; they often appear in reasoning-type questions even if the diagram looks simple.

Ready to Test Your Mastery?

50 questions  ·  Elapsed timer  ·  Instant scored results

⚡ Begin Quadrilaterals Quiz
🎯 Knowledge Check

Maths — QUADRILATERALS

50 Questions Class 9 MCQs
1
The sum of the angles of a quadrilateral is always
2
In a parallelogram, opposite sides are
3
Diagonals of a rectangle are
4
Each angle of a rectangle is
5
The diagonals of a rhombus are
6
A square is
7
The line segment joining the mid-points of two sides of a triangle is
8
In a parallelogram ABCD, if \(\angle A = 70^\circ\), then \(\angle C\) = ?
9
In a parallelogram ABCD, if \(\angle A = 110^\circ\), then \(\angle B\) = ?
10
A kite has
11
In a trapezium, only one pair of opposite sides is
12
Which of the following always has four right angles?
13
The diagonals of a square are
14
Which quadrilateral has all sides equal but no right angle?
15
The diagonals of a parallelogram bisect each other. This property helps prove a quadrilateral is a
16
Opposite angles of a cyclic quadrilateral are
17
If a quadrilateral is both a rectangle and a rhombus, then it is a
18
The diagonals of a parallelogram divide it into
19
The figure formed by joining the midpoints of the sides of a quadrilateral is always a
20
In a parallelogram, if one angle is right, then the parallelogram is a
21
The opposite sides of a parallelogram are
22
The diagonals of a rhombus
23
A quadrilateral with one pair of opposite sides parallel is
24
The number of diagonals in a quadrilateral is
25
In a parallelogram, if diagonals are equal, it is a
26
A square is a
27
The opposite angles of a parallelogram are
28
The sum of the exterior angles of any polygon is
29
A parallelogram with all sides equal is a
30
Which of these is NOT a property of a parallelogram?
31
Which of these quadrilaterals has diagonals of unequal length?
32
A parallelogram has diagonals equal in length. It must be a
33
In a rectangle ABCD, diagonal AC = BD = 10 cm. Then the length of AC is
34
The sum of adjacent angles in a parallelogram is
35
In a rhombus, the diagonals
36
The figure whose all sides and angles are equal is a
37
The diagonals of a rectangle divide it into
38
A parallelogram with perpendicular diagonals is a
39
A quadrilateral with one pair of opposite sides parallel and equal is
40
If all angles of a parallelogram are equal, then it is a
41
Which statement is true for every quadrilateral?
42
Which quadrilateral has only one pair of opposite sides equal?
43
The diagonals of a kite are
44
If the diagonals of a quadrilateral bisect each other, it is a
45
If both pairs of opposite sides of a quadrilateral are equal, it is a
46
A parallelogram with diagonals equal and perpendicular is a
47
In a parallelogram ABCD, if diagonal AC = diagonal BD, then \(\angle A\) = ?
48
Which of the following is not a parallelogram?
49
In any quadrilateral, the number of diagonals drawn from a single vertex is
50
The mid-point theorem is used to prove
📚
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Frequently Asked Questions

A quadrilateral is a closed figure with four sides, four angles, and four vertices. The sum of all interior angles of a quadrilateral is \(360^\circ\).

Parallelogram, Rectangle, Rhombus, Square, Trapezium, and Kite.

Opposite sides are equal and parallel, opposite angles are equal, and diagonals bisect each other.

The sum of all interior angles of a quadrilateral \(= 360^\circ\).

A quadrilateral whose opposite sides are parallel is called a parallelogram.

A rectangle is a parallelogram with all angles equal to \(90^\circ\).

Opposite sides are equal and parallel, all angles are \(90^\circ\), and diagonals are equal and bisect each other.

All sides are equal, opposite angles are equal, diagonals bisect each other at right angles.

All sides are equal, all angles are \(90^\circ\), diagonals are equal, and bisect each other at right angles.

A quadrilateral with one pair of opposite sides parallel is called a trapezium.

A trapezium in which the non-parallel sides are equal in length.

A quadrilateral with two pairs of adjacent sides equal and diagonals intersecting at right angles.

The line segment joining the midpoints of two sides of a triangle is parallel to the third side and half of its length.

A line drawn through the midpoint of one side of a triangle parallel to another side bisects the third side.

(i) Opposite sides are equal, <br>(ii) Opposite sides are parallel,<br> (iii) Diagonals bisect each other, <br>(iv) One pair of opposite sides is equal and parallel.

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