Exploring Some Geometric Themes — Class 8 Mathematics NCERT Solutions (Free)

Free step-by-step NCERT solutions for Class 8 Mathematics chapter "Exploring Some Geometric Themes" — 8 important questions with detailed answers for CBSE board exam preparation.

TL;DR: Free step-by-step NCERT solutions for Class 8 Mathematics chapter "Exploring Some Geometric Themes" — 8 important questions with detailed answers for…

By Syllab.in · Updated Jun 14, 2026

Key Questions Covered:

Construct a line segment AB of length 5 cm. What is the procedure?
How do you construct the perpendicular bisector of a line segment?
Construct an angle of 60° using compass and straightedge.
What is the order of rotational symmetry of a square?
How many lines of symmetry does a rectangle have?
Construct a triangle ABC with sides AB = 4 cm, BC = 5 cm, and AC = 6 cm.
+ 2 more questions in the full chapter

Solutions Summary:

Question	Status
Construct a line segment AB of length 5 cm. What is the p…	✓ Solved
How do you construct the perpendicular bisector of a line…	✓ Solved
Construct an angle of 60° using compass and straightedge.	✓ Solved
What is the order of rotational symmetry of a square?	✓ Solved
How many lines of symmetry does a rectangle have?	✓ Solved
Construct a triangle ABC with sides AB = 4 cm, BC = 5 cm,…	✓ Solved

Showing 6 of 8 questions

Q1: Construct a line segment AB of length 5 cm. What is the procedure?

Step 1: Place the ruler on paper. Step 2: Mark point A at 0 cm mark on the ruler. Step 3: Mark point B at 5 cm mark on the ruler. Step 4: Use a pencil to draw a straight line connecting A and B. Step 5: AB = 5 cm (the required line segment)

Q2: How do you construct the perpendicular bisector of a line segment?

Step 1: Given line segment AB. Step 2: Set compass to more than half the length of AB. Step 3: Draw arcs with center A, one above and one below the line. Step 4: With the same compass width, draw arcs with center B, intersecting the previous arcs. Step 5: Label intersection points as P and Q. Step 6: Draw line PQ—this is the perpendicular bisector of AB.

Q3: Construct an angle of 60° using compass and straightedge.

Step 1: Draw a line and mark point O on it. Step 2: With O as center, draw an arc of any radius intersecting the line at point A. Step 3: With the same radius and A as center, draw an arc intersecting the first arc at point B. Step 4: Draw a straight line from O through B. Step 5: Angle AOB = 60°

Q4: What is the order of rotational symmetry of a square?

Step 1: Rotational symmetry means the shape looks the same after rotation. Step 2: A square looks identical after rotation by 90°, 180°, 270°, and 360°. Step 3: The shape matches its original position 4 times in a complete 360° rotation. Step 4: Order of rotational symmetry = 4

Q5: How many lines of symmetry does a rectangle have?

Step 1: A line of symmetry divides a shape into two identical halves. Step 2: A rectangle has 1 horizontal line of symmetry (through the middle length). Step 3: A rectangle has 1 vertical line of symmetry (through the middle width). Step 4: The diagonals of a rectangle are NOT lines of symmetry. Step 5: Total lines of symmetry = 2

Q6: Construct a triangle ABC with sides AB = 4 cm, BC = 5 cm, and AC = 6 cm.

Step 1: Draw a line and mark point A. Step 2: Using ruler, mark point B at 4 cm from A. (AB = 4 cm) Step 3: With compass set to 5 cm, center at B, draw an arc above the line. Step 4: With compass set to 6 cm, center at A, draw an arc intersecting the previous arc. Label this point C. Step 5: Draw lines AC and BC. Step 6: Triangle ABC is constructed with the given side lengths.

Showing 6 of 8 questions. Visit the full page for complete solutions.