Quadrilaterals — Class 9 MCQs with Answers
Class 9 CBSE Mathematics · Chapter 12
90 practice questions · 30 Easy · 30 Medium · 30 Hard · Updated
Practise the most important Class 9 CBSE Mathematics questions from Chapter 12, "Quadrilaterals". You get 9 timed quizzes made from 90 NCERT-based MCQs, with answers and explanations. The questions are split into 30 Easy, 30 Medium and 30 Hard. Warm up on the basics, then move on to the exam-level questions that top scorers in CBSE Board exams and the JEE & NEET foundation years get right.
To score well in "Quadrilaterals", focus on fast problem-solving, formula recall and step-by-step working. Each MCQ here is timed and uses exam-style marking (+4 correct, −1 wrong, 0 skipped). This helps you stay accurate when time is short, just as real papers need. Every question has a short explanation, so a wrong answer becomes a quick lesson. It is the fastest way to fix gaps before a test.
Use this chapter for focused revision. Start with the Easy set to check your basics on Quadrilaterals, then move to Medium and Hard to practise applying them. Your accuracy, streaks and XP save automatically. This chapter also adds to your overall Class 9 Mathematics mastery score. 14 sample questions are solved in full below, with the answer and a worked explanation. Sign in free to start practising.
Quadrilaterals — important questions & MCQs with answers (Class 9 Mathematics)
14 solved questions from this chapter's difficulty levels, each with its answer and explanation.
- Q1Easy
By the book's definition, when do the points on segments AB, BC, CD and DA form quadrilateral ABCD?
A.When the four points are distinct, lie in one plane, and every non-vertex point lies on exactly one segment✓ CorrectB.When the four points are distinct and all four segments have the same lengthC.When the four points are distinct and no two of the four segments are parallelD.When the four points are distinct and all of them lie on one circleAnswer: A. When the four points are distinct, lie in one plane, and every non-vertex point lies on exactly one segment
Explanation: The definition needs four distinct points in one plane, and every point except the vertices must lie on exactly one segment. This rules out collinear vertices, overlapping sides and self-crossing; equal lengths or parallel sides play no part.
- Q2Easy
Theorem 1 of the chapter lists three properties of every parallelogram. Which set is correct?
A.Opposite sides are equal, opposite angles are equal, and the diagonals bisect each other✓ CorrectB.All sides are equal, opposite angles are equal, and the diagonals are perpendicularC.Opposite sides are equal, and the diagonals are equal and bisect each otherD.Adjacent angles are equal, opposite sides are parallel, and diagonals are equalAnswer: A. Opposite sides are equal, opposite angles are equal, and the diagonals bisect each other
Explanation: Every parallelogram has equal opposite sides, equal opposite angles and diagonals that bisect each other. Equal sides belong to a rhombus and equal diagonals to a rectangle, not to every parallelogram.
- Q3Easy
P and Q are the midpoints of sides AB and AC of triangle ABC. What does the Midpoint Theorem say?
A.PQ ⊥ BC and PQ = BC/2B.PQ ∥ BC and PQ = 2 × BCC.PQ ∥ AB and PQ = AC/2D.PQ ∥ BC and PQ = BC/2✓ CorrectAnswer: D. PQ ∥ BC and PQ = BC/2
Explanation: The segment joining the midpoints of two sides is parallel to the third side and half as long. It is half of BC, not double, and it is parallel to BC, not perpendicular.
- Q4Easy
A median of a triangle is the segment that joins:
A.a vertex to the midpoint of the opposite side✓ CorrectB.the midpoints of two sidesC.a vertex to the foot of the perpendicular on the opposite sideD.two vertices of the triangleAnswer: A. a vertex to the midpoint of the opposite side
Explanation: A median runs from a vertex to the midpoint of the opposite side, like AR, BQ and CP in the book. The segment from a vertex to the foot of the perpendicular is an altitude, not a median.
- Q5Easy
The midpoints of the four sides of any quadrilateral are joined in order. What shape is always formed?
A.A rectangleB.A rhombusC.A parallelogram✓ CorrectD.A shape similar to the original quadrilateralAnswer: C. A parallelogram
Explanation: Theorem 9 says the midpoints of the four sides form a parallelogram, called the Varignon parallelogram. It is a rectangle or rhombus only in special cases.
- Q6Easy
What does it mean to tile the plane with a shape?
A.To cover the plane using square tiles onlyB.To draw the shape so that it has a line of symmetryC.To cover the plane with copies that may overlap but leave no gapsD.To cover the plane with copies of the shape, with no gaps and no overlaps✓ CorrectAnswer: D. To cover the plane with copies of the shape, with no gaps and no overlaps
Explanation: A tiling covers the whole plane with copies of the given shape or shapes, leaving no gaps and making no overlaps. Overlaps are not allowed, and any shape can be tried, not only squares.
- Q7Medium
Quadrilateral ABCD can be named by tracing its vertices in order. Which of these is NOT another name for ABCD?
A.CDABB.ACBD✓ CorrectC.DCBAD.BADCAnswer: B. ACBD
Explanation: Valid names go round the boundary in either direction from any vertex: BCDA, CDAB, DABC, DCBA, ADCB, BADC, CBAD. ACBD jumps along the diagonal AC, so it traces a different, self-intersecting figure.
- Q8Medium
The chapter restates Theorem 3 as: 'If each pair of adjacent angles in quadrilateral ABCD ___, then ABCD is a parallelogram.' What fills the blank?
A.is equalB.adds up to 90°C.adds up to 180°✓ CorrectD.adds up to 360°Answer: C. adds up to 180°
Explanation: Equal opposite angles with a total of 360° force each adjacent pair to add to 180°, and the converse also holds. Adjacent angles adding to 180° make each pair of opposite sides parallel.
- Q9Medium
In triangle ABC, P and Q are the midpoints of AB and AC, and PQ = 4.5 cm. Find BC.
A.9 cm✓ CorrectB.2.25 cmC.4.5 cmD.13.5 cmAnswer: A. 9 cm
Explanation: PQ = BC/2, so BC = 2 × 4.5 = 9 cm. Halving PQ instead of doubling it gives 2.25 cm.
- Q10Medium
G is the centroid of triangle ABC, and on median BE the part GE is 4 cm. Find the length of BE.
A.8 cmB.12 cm✓ CorrectC.6 cmD.16 cmAnswer: B. 12 cm
Explanation: BG : GE = 2 : 1, so BG = 8 cm and BE = 8 + 4 = 12 cm. 8 cm is only BG, the longer part.
- Q11Medium
The diagonals of quadrilateral ABCD are AC = 10 cm and BD = 14 cm. What is the perimeter of its Varignon parallelogram?
A.24 cm✓ CorrectB.48 cmC.12 cmD.20 cmAnswer: A. 24 cm
Explanation: Two sides of the Varignon parallelogram are AC/2 = 5 cm and two are BD/2 = 7 cm, so the perimeter is 2(5 + 7) = 24 cm, which equals AC + BD. 48 cm forgets that each side is half a diagonal.
- Q12Hard
A, B, C are non-collinear. The full lines AB, BC and CA split the rest of the plane into 7 regions. A point D is placed inside one region. Over the 7 regions, how does ABCD turn out?
A.Convex in 1 region, self-intersecting in 3 regions, non-convex in 3 regionsB.Convex in 3 regions, self-intersecting in 3 regions, non-convex in 1 regionC.Convex in 1 region, self-intersecting in 0 regions, non-convex in 6 regionsD.Convex in 1 region, self-intersecting in 2 regions, non-convex in 4 regions✓ CorrectAnswer: D. Convex in 1 region, self-intersecting in 2 regions, non-convex in 4 regions
Explanation: D beyond side AC (opposite B) makes the diagonals cross: convex. D beyond side AB or side BC makes side CD cross AB or side DA cross BC: self-intersecting. D inside the triangle or in any of the 3 corner regions puts one vertex inside the triangle of the other three: non-convex.
- Q13Hard
Which ONE of these statements is FALSE?
A.A parallelogram with one right angle is a rectangleB.A parallelogram with equal diagonals is a rectangleC.A rhombus with perpendicular diagonals is a square✓ CorrectD.A quadrilateral whose diagonals bisect each other at right angles is a rhombusAnswer: C. A rhombus with perpendicular diagonals is a square
Explanation: The diagonals of every rhombus are perpendicular, so this gives no new information; a rhombus is a square only if it also has a right angle or equal diagonals. The other three statements are true.
- Q14Hard
ABCD is a trapezium with AD ∥ BC, AD = 3 cm and BC = 5 cm. E and F are the midpoints of AB and DC. Find the ratio area(AEFD) : area(EBCF).
A.7 : 9✓ CorrectB.3 : 5C.1 : 1D.9 : 7Answer: A. 7 : 9
Explanation: EF = (3 + 5)/2 = 4 cm, and EF cuts the height h into two halves. So the areas are (3 + 4)/2 × h/2 and (4 + 5)/2 × h/2, in the ratio 7 : 9. Equal heights do not mean equal areas, because the parallel sides differ.
Key concepts: Quadrilaterals (Class 9 Mathematics)
This chapter defines a quadrilateral (4-gon) exactly and sorts out convex, non-convex and self-intersecting shapes. It proves the converse tests for parallelograms, then uses parallelograms to prove the Midpoint Theorem, the Centroid Theorem and Varignon's theorem, and ends by showing that any 4-gon can tile the plane.
- Definition of a quadrilateral
- Four distinct points A, B, C, D in a plane form quadrilateral ABCD when every point of segments AB, BC, CD, DA other than the vertices lies on exactly one segment. This rules out three collinear vertices, overlapping sides and self-crossing.
- Non-planar and self-intersecting 4-gons
- A 4-gon like BENT whose vertices are not in one plane is non-planar; one like CUTS whose sides cross is self-intersecting. Both occur in real 4-bar linkages, but 'quadrilateral' normally means planar and not self-intersecting.
- Parts and names of a quadrilateral
- ABCD has sides AB, BC, CD, DA and diagonals AC, BD; adjacent sides share a vertex and opposite sides do not. It has exactly 8 names (ABCD, BCDA, CDAB, DABC, DCBA, ADCB, BADC, CBAD); ACBD is a different figure.
- Convex and non-convex
- A quadrilateral is convex when all internal angles are less than 180°, or equivalently when its diagonals intersect. A non-convex one, like DART, has one angle more than 180° (a dent) and its diagonals do not meet.
- CPCT
- Corresponding parts of congruent triangles are equal. Once two triangles are shown congruent (by SSS, SAS or ASA), every matching side and angle is equal — this is the 'by congruence' step in the chapter's parallelogram proofs.
- Parallelogram properties (Theorem 1)
- In a parallelogram, opposite sides are equal, opposite angles are equal, adjacent angles add to 180°, and the diagonals bisect each other. The proofs use ∆ACD ≅ ∆CAB by ASA and alternate or co-interior angles.
- Converse tests (Theorems 2, 3, 4)
- All three converses are true: equal opposite sides (proof by SSS), equal opposite angles (adjacent pairs then add to 180°), or diagonals that bisect each other (proof by SAS) each make a quadrilateral a parallelogram.
- Equal parallel sides test (Theorem 5)
- If ONE pair of opposite sides is both equal and parallel, the quadrilateral is a parallelogram. One pair parallel and the other pair equal is not enough: an isosceles trapezium shows this.
- Statement vs converse
- A converse swaps the 'if' and 'then' parts, and its truth must be proved separately: 'x = y ⇒ x² = y²' is true but its converse fails for x = 3, y = −3. A proof can sometimes be run backwards with new reasons.
- Midpoint Theorem (Theorem 6)
- The segment joining the midpoints of two sides of a triangle is parallel to the third side and half its length. The proof draws a line through C parallel to BA and uses AAS congruence plus the equal parallel sides test.
- Converse of the Midpoint Theorem (Theorem 7)
- A line through the midpoint of one side of a triangle, parallel to a second side, bisects the third side and cuts off a segment half the parallel side. One proof uses the fact that only one line through a point is parallel to a given line.
- Four congruent triangles and the trapezium midline
- Joining the three side midpoints cuts a triangle into four congruent half-size copies, each with a quarter of the area. In a trapezium, the segment joining midpoints of the non-parallel sides is parallel to them and equals half the sum of the parallel sides.
- Centroid Theorem (Theorem 8)
- The three medians of a triangle are concurrent at the centroid, which divides each median 2 : 1 with the longer part at the vertex. The proof takes midpoints X, Y of BM and CM and shows the median is cut into three equal parts.
- Varignon parallelogram (Theorem 9)
- The midpoints of the four sides of any quadrilateral form a parallelogram whose sides are parallel to the diagonals and half as long. It is a rhombus if AC = BD, a rectangle if AC ⊥ BD, and a square if both hold.
- Tiling the plane with any 4-gon
- Angles around any vertex of a tiling add to 360°, and a 4-gon's angles also add to 360°, so four copies fit round a point. Method 1 turns copies 180° about edge midpoints; Method 2 builds on the grid of Varignon parallelograms; a regular pentagon (108°) cannot tile.
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Start this chapter free →Quadrilaterals — FAQs
What are the key concepts in Class 9 Mathematics Quadrilaterals?+
This chapter defines a quadrilateral (4-gon) exactly and sorts out convex, non-convex and self-intersecting shapes. It proves the converse tests for parallelograms, then uses parallelograms to prove the Midpoint Theorem, the Centroid Theorem and Varignon's theorem, and ends by showing that any 4-gon can tile the plane. Key ideas include Definition of a quadrilateral, Non-planar and self-intersecting 4-gons, Parts and names of a quadrilateral, Convex and non-convex, CPCT, Parallelogram properties (Theorem 1).
What does Class 9 Mathematics Chapter 12 (Quadrilaterals) cover on XamBaaz?+
It has 90 NCERT-based MCQs on "Quadrilaterals": 30 Easy, 30 Medium and 30 Hard. Together they make 9 timed quizzes, and you never get the same set twice. Every question has an instant explanation. They help you prepare for CBSE Board exams and the JEE & NEET foundation years.
Are these "Quadrilaterals" questions free to practise?+
Yes. Sign in with Google to practise "Quadrilaterals" free. Full unlimited access is ₹999/year. One year from the day you pay. You stay in Class 9 till 31 March; on 1 April your account moves up to Class 10 and the rest of your year carries over. No chapter is charged separately.
How should I revise "Quadrilaterals" for the exam?+
Start with the Easy quiz to check your basics, then try Medium and Hard to practise applying them. There are 9 timed quizzes on this chapter, so you can come back for a fresh set instead of one you have seen. Read each explanation, retry the questions you miss, and track your accuracy until it stays high.
Are these "Quadrilaterals" MCQs available with answers?+
Yes. 14 sample questions are shown here in full, each with the correct option and a step-by-step "Why" explanation. Sign in free with Google to start practising, with instant scoring.
Is there negative marking in the "Quadrilaterals" quizzes?+
Yes. The timed quizzes use exam-style marking: +4 for a right answer, −1 for a wrong one and 0 for a skip. MHT-CET and CBSE board papers have no negative marking. Our mocks for those are scored their way.
What are the important questions from Quadrilaterals (Class 9 Mathematics)?+
The questions that matter most test Definition of a quadrilateral, Non-planar and self-intersecting 4-gons, Parts and names of a quadrilateral, Convex and non-convex, CPCT, Parallelogram properties (Theorem 1). This page shows 14 solved important MCQs with answers and explanations. Sign in to practise all 90 questions on the chapter as timed quizzes.
Is there an online quiz for Quadrilaterals?+
Yes — Class 9 Mathematics Quadrilaterals has timed online quizzes at Easy, Medium and Hard levels, with instant scoring and a worked explanation on every question. The first quiz on the chapter is free.