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Class 9 Maths: Quadrilaterals, 8 practice questions with answers

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These are 8 practice questions on Chapter 12, Quadrilaterals, of the new NCERT Class 9 Maths textbook, Ganita Manjari, Part II (First Edition, August 2026). Each has a worked answer and the textbook page it comes from. They cover telling a convex quadrilateral from a non-convex one, three tests for a parallelogram, the Midpoint Theorem and its converse, the Centroid Theorem, and the parallelogram formed by the midpoints of a quadrilateral. Try each one on paper before you open the answer.

These questions are our own, drafted with AI help. Every number was re-computed by a test script and none of the numbers is taken from the chapter, but no practising teacher has reviewed them yet. If you find a mistake, please tell us.

What the chapter says you need

Facts from the NCERT textbook (Ganita Manjari, Grade 9, Part II, Chapter 12, printed pages 51 to 84):

Convex or not, and parallelogram tests

Question 1. A quadrilateral has angles 41°, 44°, 229° and 46°. Check that these can be the angles of a quadrilateral, and say whether it is convex.

Answer: yes, they add to 360°; it is not convex. 41 + 44 + 229 + 46 = 360, as the angles of a quadrilateral must. One angle, 229°, is more than 180°, so the quadrilateral has a dent and is non-convex. (Angle sum, page 59; convex quadrilaterals, page 54.)

Question 2. In quadrilateral ABCD, ∠A = 86°, ∠B = 94° and ∠C = 86°. Find ∠D. Is ABCD a parallelogram?

Answer: ∠D = 94°; yes. ∠D = 360° − (86° + 94° + 86°) = 360° − 266° = 94°. Now ∠A = ∠C = 86° and ∠B = ∠D = 94°: both pairs of opposite angles are equal, so ABCD is a parallelogram by Theorem 3. As a check, adjacent angles add to 86° + 94° = 180°. (Theorem 3, pages 58 and 59.)

Question 3. The diagonals PR and QS of quadrilateral PQRS meet at O, with PO = 4.7 cm, OR = 4.7 cm, QO = 6.3 cm and OS = 6.3 cm. Is PQRS a parallelogram? Which test did you use?

Answer: yes, by the diagonals test. O is the midpoint of PR (PO = OR = 4.7 cm) and of QS (QO = OS = 6.3 cm), so the diagonals bisect each other. A quadrilateral whose diagonals bisect each other is a parallelogram (Theorem 4). (Page 59.)

Question 4. In quadrilateral WXYZ, side WX is parallel to side ZY and WX = ZY = 37 mm. Is WXYZ a parallelogram? What can you then say about sides XY and WZ?

Answer: yes; XY = WZ, and XY ‖ WZ. One pair of opposite sides is both equal and parallel, so WXYZ is a parallelogram by the equal parallel sides test (Theorem 5). In a parallelogram the other pair of opposite sides is also parallel and equal. (Theorem 5, page 59; opposite sides of a parallelogram, page 56.)

Midpoints and medians

Question 5. A triangle has sides 86 mm, 94 mm and 98 mm. The midpoints of its three sides are joined to make a smaller triangle. Find the sides and the perimeter of the smaller triangle.

Answer: 43 mm, 47 mm and 49 mm; perimeter 139 mm. By the Midpoint Theorem, each segment joining two midpoints is half the third side: 86 ÷ 2 = 43, 94 ÷ 2 = 47, 98 ÷ 2 = 49 mm. Perimeter = 43 + 47 + 49 = 139 mm, which is half of the original perimeter 86 + 94 + 98 = 278 mm. (Midpoint Theorem, page 63.)

Question 6. In triangle ABC, AC = 182 mm and BC = 196 mm. P is the midpoint of AB. The line through P parallel to BC meets AC at Q. Find AQ, QC and PQ.

Answer: AQ = QC = 91 mm; PQ = 98 mm. By the converse of the Midpoint Theorem, the line through P parallel to BC bisects AC, so AQ = QC = 182 ÷ 2 = 91 mm, and PQ is half of BC: 196 ÷ 2 = 98 mm. (Theorem 7, page 64.)

Question 7. A median of a triangle is 141 mm long. How far is the centroid from the vertex at one end of this median, and how far from the midpoint at the other end?

Answer: 94 mm from the vertex; 47 mm from the midpoint. The centroid divides each median in the ratio 2 : 1, with the longer part towards the vertex. So the median is split into 3 equal parts of 141 ÷ 3 = 47 mm: the vertex part is 2 × 47 = 94 mm and the other part is 47 mm. Check: 94 + 47 = 141. (Centroid Theorem, page 66.)

Question 8. A quadrilateral has diagonals of 172 mm and 194 mm. The midpoints of its four sides are joined. What shape do they form, how long are its sides, and what is its perimeter?

Answer: a parallelogram with sides 86 mm and 97 mm; perimeter 366 mm. The midpoints form the Varignon parallelogram. Each of its sides joins the midpoints of two sides of a triangle cut off by a diagonal, so by the Midpoint Theorem it is parallel to that diagonal and half as long: 172 ÷ 2 = 86 mm and 194 ÷ 2 = 97 mm. Perimeter = 86 + 97 + 86 + 97 = 366 mm, equal to the sum of the two diagonals, 172 + 194. (Varignon parallelogram, Theorem 9 and its reasoning, page 67; Midpoint Theorem, page 63.)

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Sources

All opened and read on 22 October 2026. Page numbers are the printed page numbers of the textbook; printed page = PDF page + 50.

The theorems are from the textbook pages above. The questions, worked answers and checks are our own, and every number was re-computed by script. This guide is general information; follow your teacher and the textbook.