Quadrilaterals Class 9 Maths Worksheet with Quiz and Activities
Work with angles, midpoints and centroids, and build a midpoint parallelogram in 2D and 3D. On WitKnowLearn you get the Quadrilaterals Class 9 online quiz, online activities and interactive games, a quadrilateral lab, a virtual lab and a worksheet-style practice sheet for NCERT Ganita Manjari Chapter 12.
Quadrilaterals Class 9 Online Quiz
20 questions: 10 easy, 5 average and 5 thinking. Tap an answer and the next question comes up.
Quadrilaterals Class 9 Activities
👆 Tap a tab to switch: Learn, Games, Labs, Challenges, Virtual Lab and Practice sheet
Quadrilaterals: the Story of Quadrilaterals
A short read for Class 9 before you play. These notes follow Chapter 12 of NCERT Ganita Manjari, Part I.
▱ Four sides
Four angles always add up to 360 degrees.
🪃 Convex or dent
A dart has an angle over 180 degrees.
▱ Parallelograms
Opposite sides and angles are equal.
📏 Midpoints
A midpoint segment is half the third side.
⚖ The centroid
Medians meet and divide 2 : 1.
🧩 Tiling
Quadrilaterals fill the plane with no gaps.
Quadrilaterals Class 9 Activities
Follow every step on the Number Train. Earn up to 3 stars in every activity.
This page follows NCERT Class 9 Maths Ganita Manjari, Part I, Chapter 12. Students work with angles, midpoints, medians and tiles of quadrilaterals.
The activities are pitched at Class 9 level. Students sort always true from not always true, pop true facts, use the Midpoint Theorem and the centroid rule, and solve case studies on tiles and trapeziums. The virtual lab builds the midpoint parallelogram in 2D and 3D. Explore more Class 9 maths worksheets on WitKnowLearn after this chapter.
Formulas and facts to know
| Figure | Key fact | Example |
|---|---|---|
| Parallelogram | A + B = 180 | 70 and 110 |
| Midpoint Theorem | PQ = BC/2 | 12 gives 6 |
| Centroid | 2 : 1 | 8 and 4 |
| Midpoint quadrilateral | Perimeter = AC + BD | 10 + 8 = 18 |
How to use this page
- Flip the six cards and try the Quadrilateral Lab in the Learn tab.
- Play the five games and the five labs to practise each idea.
- Finish the five challenges to collect up to 15 points.
- Build the midpoint parallelogram in the Virtual Lab and look at it in 2D and 3D.
- Take the 20-question online quiz, with assertion and reason and case study questions, and fill in the practice sheet.
Worked examples
180 - 70 = 110 degrees.
AG = 2/3 x 12 = 8 cm.
5 + 4 + 5 + 4 = 18 cm.
This Quadrilaterals worksheet for Class 9 maths gives you online activities and interactive games that make the chapter clear. Every activity has a goal, a hint and a short fact, so students learn while they enjoy.
Complete Guide: NCERT Class 9 Maths Quadrilaterals Chapter 12
This guide is for Class 9 students, parents and teachers. It covers Chapter 12 of NCERT Ganita Manjari, Part I, and shows how to use the quiz, labs and games on this page.
Introduction to Quadrilaterals
The chapter studies quadrilaterals, parallelograms, the Midpoint Theorem, the centroid and how quadrilaterals tile the plane.
What is there in this chapter
- Convex and non-convex quadrilaterals.
- Angle sum of a quadrilateral.
- Parallelograms and their properties.
- The Midpoint Theorem.
- The centroid of a triangle.
- The midpoint quadrilateral.
- Tiling the plane.
Learning objectives
- Find angles of quadrilaterals.
- Use properties of parallelograms.
- Apply the Midpoint Theorem.
- Use the centroid ratio 2 : 1.
- Reason with assertions and case studies.
Learning outcomes
- The student can find that angle B is 110 degrees when angle A is 70 degrees.
- The student can find that PQ is 6 cm when BC is 12 cm.
- The student can find that AG is 8 cm when AD is 12 cm.
- The student can find that the midpoint quadrilateral of diagonals 10 and 8 has perimeter 18.
Quadrilaterals Class 9 resources on this page
| Resource | What it gives |
|---|---|
| Online quiz | 20 questions: 10 easy, 5 average and 5 thinking, with assertion and reason and case study questions and a full review |
| Flip cards | 6 picture cards with one-line rules |
| Quadrilateral Lab | A hands-on lab with 3 rounds |
| Games | 5 interactive games |
| Labs | 5 activity labs |
| Virtual Lab | 2 experiments and a 2D and 3D midpoint parallelogram builder with aim, procedure, observations and conclusion |
| Challenges | 5 challenges, 15 points in all |
| Practice sheet | A worksheet-style sheet with 16 questions, name and date lines and a live score |
Key facts
| Idea | Rule |
|---|---|
| Angle sum | 360 degrees |
| Parallelogram | A + B = 180 |
| Midpoint Theorem | PQ = BC/2 |
| Centroid | 2 : 1 |
| Varignon | Midpoints give a parallelogram |
| Tiling | Angles fill 360 |
Types of questions you may see
- Find angles.
- Use the Midpoint Theorem.
- Use the centroid ratio.
- Find the midpoint quadrilateral.
- Assertion and reason questions.
- Case studies on tiles and trapeziums.
Solved examples
110.
6.
8.
18.
45.
14.
Common mistakes
| Mistake | Correct idea |
|---|---|
| Thinking AB = CD makes a parallelogram. | An isosceles trapezium has AB = CD. |
| Taking the centroid as the midpoint of a median. | It divides the median 2 : 1. |
| Using angle sum 180 for a quadrilateral. | It is 360. |
| Thinking pentagons tile the plane. | 108 does not divide 360. |
| Assuming all diagonals cross. | Not in a non-convex quadrilateral. |
Quadrilaterals in daily life
Tilers, builders and designers use quadrilaterals and tilings, and engineers use midpoints and centroids to balance structures.
Tips for parents and teachers
- Draw the figure and mark equal parts.
- Check that angles add up to 360.
- Look for a midpoint before using the theorem.
- Practise one assertion and one case study each week.
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Quadrilaterals Class 9 FAQs
What is Chapter 12 of NCERT Class 9 Maths Ganita Manjari?
Chapter 12 is Quadrilaterals. It covers convex and non-convex quadrilaterals, parallelograms, the Midpoint Theorem, the centroid of a triangle, the midpoint quadrilateral and tiling the plane.
What is a convex quadrilateral?
A convex quadrilateral has every angle less than 180 degrees and its diagonals cross inside it. A non-convex quadrilateral has one angle greater than 180 degrees, like a dart.
What is the angle sum of a quadrilateral?
The four angles add up to 360 degrees, because a diagonal splits the quadrilateral into two triangles.
What are the properties of a parallelogram?
Opposite sides are parallel and equal, opposite angles are equal, adjacent angles add up to 180 degrees and the diagonals bisect each other.
How do we prove a quadrilateral is a parallelogram?
Show any one of these: both pairs of opposite sides equal, both pairs of opposite angles equal, diagonals that bisect each other, or one pair of opposite sides equal and parallel.
What is the Midpoint Theorem?
The segment joining the midpoints of two sides of a triangle is parallel to the third side and equal to half of it. If P and Q are midpoints of AB and AC, then PQ = BC/2.
What is the centroid of a triangle?
The centroid is the point where the three medians meet. It divides each median in the ratio 2 : 1 from the vertex, so AG = 2/3 of AD.
What is the midpoint quadrilateral?
Joining the midpoints of the sides of any quadrilateral in order gives a parallelogram. Its perimeter is the sum of the diagonals of the original.
What is the midline of a trapezium?
The segment joining the midpoints of the non-parallel sides is parallel to the bases and equals half of their sum. For bases 18 and 10 it is 14.
Which regular polygons tile the plane?
Only those whose angle divides 360 degrees: the equilateral triangle, the square and the regular hexagon. A regular pentagon has angle 108 degrees, which does not divide 360.
Can any quadrilateral tile the plane?
Yes. Four copies of any quadrilateral, one with each angle, meet at a point because the angles add up to 360 degrees.
What can students do on this page?
Students can take a 20-question online quiz with assertion and reason and case study questions, play five games, try five online activities, finish five challenges, run the Quadrilateral Lab, do two virtual experiments, build the midpoint parallelogram in 2D and 3D, and fill in a 16-question practice sheet with a Show answers button.
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