How many practice questions are available for Rectilinear Figures?

SparkEd Math offers 60+ practice questions for Rectilinear Figures across 3 difficulty levels (Easy, Medium, Hard) plus a timed test mode. Each question comes with visual step-by-step solutions and AI coaching hints.

Is Rectilinear Figures content free on SparkEd Math?

Yes! All Rectilinear Figures content on SparkEd Math is 100% free, including practice questions, visual solutions, lessons, and AI coaching. No credit card required.

How does SparkEd Math teach Rectilinear Figures differently from textbooks?

SparkEd Math uses visual step-by-step solutions for every Rectilinear Figures problem, making complex concepts easy to understand. The platform includes 3 difficulty levels for progressive learning, a Super Power Help AI coach for instant doubt-clearing, and interactive practice rather than passive reading.

Is SparkEd's Rectilinear Figures content aligned with the ICSE syllabus?

Yes, all Rectilinear Figures questions and lessons on SparkEd Math are fully aligned with the Indian Certificate of Secondary Education (ICSE) syllabus for Class 9. The content follows the official curriculum structure and exam pattern.

Rectilinear Figures — Class 9 ICSE (2025-26)

About Rectilinear Figures — Class 9 ICSE

Study properties and theorems of parallelograms, rectangles, rhombuses, and squares. This topic is part of the ICSE Class 9 mathematics syllabus (chapter: Chapter 11). On this page you can practice 60 questions across three difficulty levels — 20 easy, 20 medium, and 20 hard — each with a visual step-by-step solution, plus a timed 35-question mastery test with a live leaderboard. Worked examples and sample questions from the topic are below.

What you'll learn in Rectilinear Figures

Introduction to Rectilinear Figures: Polygons and Quadrilaterals
The Parallelogram: Properties and Applications
Special Parallelograms: Rectangles and Rhombuses
The Square and Introduction to Trapeziums
Summary, Proving Properties, and Exam Preparation

Interactive lesson · about 15 minutes · checkpoint question after every unit

Rectilinear Figures — solved examples for Class 9 ICSE

Example 1easy

Which of the following statements is true regarding a regular polygon?

A)A) All its sides are equal in length, and all its interior angles are equal.
B)B) Only its sides are equal in length, but its angles can be different.
C)C) Only its interior angles are equal, but its sides can be different lengths.
D)D) It must have at least five sides.

Step-by-step solution

A polygon is a closed figure made up of line segments.
A regular polygon is defined as a polygon that is both equiangular (all interior angles are equal) and equilateral (all sides are equal in length).
Therefore, statement A accurately describes a regular polygon.

Answer: A) All its sides are equal in length, and all its interior angles are equal.

Example 2medium

The angles of a hexagon are (x+5)°, (2x-10)°, (x+15)°, (3x-25)°, (x+10)° and (x+5)°. Find the value of x.

A)A) 70
B)B) 75
C)C) 80
D)D) 85

Step-by-step solution

The sum of interior angles of an n-sided polygon is given by the formula (n-2) × 180°.
For a hexagon, n=6, so the sum of interior angles = (6-2) × 180° = 4 × 180° = 720°.
Sum the given angles: (x+5) + (2x-10) + (x+15) + (3x-25) + (x+10) + (x+5) = (x+2x+x+3x+x+x) + (5-10+15-25+10+5) = 9x + 0 = 9x.
Equate the sum to 720°: 9x = 720. Solving for x, we get x = 720 / 9 = 80.

Answer: C) 80

Example 3hard

A quadrilateral has its diagonals bisecting each other. Which of the following statements must always be true about this quadrilateral?

A)It is a rhombus.
B)It is a rectangle.
C)It is a parallelogram.
D)It is a square.

Step-by-step solution

A key property of a parallelogram is that its diagonals bisect each other.
Conversely, a fundamental theorem states that if the diagonals of a quadrilateral bisect each other, then the quadrilateral must be a parallelogram.
Rhombus, rectangle, and square are special types of parallelograms that require additional properties (e.g., equal diagonals for rectangle, perpendicular diagonals for rhombus, both for square) which are not guaranteed by the given condition.

Answer: It is a parallelogram.

Practice questions on Rectilinear Figures

Q1.easy
What is the sum of the interior angles of a hexagon?
1. A)A) 360°
2. B)B) 720°
3. C)C) 900°
4. D)D) 1080°
Show answer
Answer: B) 720°
Hint: Remember the formula for the sum of interior angles of a polygon with 'n' sides.
Q2.easy
Which of the following statements is true about the sum of the exterior angles of any convex polygon?
1. A)A) It depends on the number of sides of the polygon.
2. B)B) It is always equal to (n-2) × 180°, where n is the number of sides.
3. C)C) It is always 360°, regardless of the number of sides.
4. D)D) It is always half the sum of its interior angles.
Show answer
Answer: C) It is always 360°, regardless of the number of sides.
Hint: This is a fundamental property that holds for all convex polygons, irrespective of their shape or number of sides.
Q3.easy
In a parallelogram ABCD, if ∠A = 70°, what is the measure of ∠B?
1. A)A) 70°
2. B)B) 90°
3. C)C) 100°
4. D)D) 110°
Show answer
Answer: D) 110°
Hint: Remember the relationship between consecutive angles in a parallelogram. They are supplementary.
Q4.medium
If each exterior angle of a regular polygon is 45°, how many sides does the polygon have?
1. A)A) 6
2. B)B) 7
3. C)C) 8
4. D)D) 9
Show answer
Answer: C) 8
Hint: The sum of the exterior angles of any convex polygon is always 360°. For a regular polygon, all exterior angles are equal.
Q5.medium
In a parallelogram ABCD, ∠A = (x + 20)° and ∠C = (2x - 40)°. Find the measure of ∠B.
1. A)A) 60°
2. B)B) 80°
3. C)C) 100°
4. D)D) 120°
Show answer
Answer: C) 100°
Hint: In a parallelogram, opposite angles are equal and consecutive angles are supplementary.
Q6.medium
The diagonals AC and BD of a parallelogram ABCD intersect at O. If AO = (3x - 1) cm and OC = (x + 7) cm, and BO = (2y + 3) cm and OD = (3y - 2) cm, find the values of x and y.
1. A)A) x=4, y=5
2. B)B) x=3, y=4
3. C)C) x=5, y=4
4. D)D) x=4, y=3
Show answer
Answer: A) x=4, y=5
Hint: Remember that the diagonals of a parallelogram bisect each other. This means they cut each other into two equal parts.
Q7.hard
In a rhombus ABCD, ∠ABC = 120°. If the diagonal BD is 8 cm, find the length of the side AB.
1. A)4 cm
2. B)8 cm
3. C)4√3 cm
4. D)8√3 cm
Show answer
Answer: 8 cm
Hint: Remember that the diagonals of a rhombus bisect its vertex angles. Consider the triangle formed by a side and a diagonal.
Q8.hard
ABCD is a rectangle. P, Q, R, S are the midpoints of sides AB, BC, CD, and DA respectively. What type of quadrilateral is PQRS?
1. A)Parallelogram
2. B)Rectangle
3. C)Rhombus
4. D)Square
Show answer
Answer: Rhombus
Hint: Apply the Midpoint Theorem to triangles formed by the sides and diagonals of the rectangle. Compare the lengths of the sides of PQRS.
Q9.hard
Ravi states: 'In any parallelogram ABCD, the bisectors of two consecutive angles, say ∠A and ∠B, always intersect at a right angle.' Is Ravi's statement correct? If not, what is the correct property or outcome?
1. A)Ravi is incorrect; they always intersect at an acute angle.
2. B)Ravi is incorrect; they always intersect at an obtuse angle.
3. C)Ravi is correct; they always intersect at 90°.
4. D)Ravi is incorrect; they only intersect at 90° if the parallelogram is a square.
Show answer
Answer: Ravi is correct; they always intersect at 90°.
Hint: In a parallelogram, what is the sum of consecutive angles? Consider the triangle formed by the angle bisectors and the side.

These are 9 of the 60 questions available for Rectilinear Figures. Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.