Class 7 Maths Chapter 7: A Tale of Three Intersecting Lines Important Questions by PW

Triangles contain several lines, sides, and angles, making it important to identify the correct geometric property while solving questions. Medians, altitudes, perpendicular lines, orthocentres, and different types of triangles can become confusing when multiple concepts appear together. Diagram-based questions may also require careful observation to find unknown angles or apply the right relationship.

The Class 7 Maths Chapter 7 Important Questions offer focused practice on A Tale of Three Intersecting Lines through MCQs and diagram-based problems. You can use them to understand triangle properties, identify important line segments, practise constructions, calculate unknown angles, and apply geometric concepts in different situations.

Important Questions for Class 7 Maths Chapter 7 A Tale of Three Intersecting Lines

Explore these Class 7 Maths Chapter 7 Important Questions to strengthen your understanding of triangle properties, angle relationships, constructions, medians, and altitudes covered in A Tale of Three Intersecting Lines.

Q1. Types of Triangles

A triangle in which all three sides are equal is called:

(A) Isosceles triangle
(B) Scalene triangle
(C) Equilateral triangle
(D) Right-angled triangle

Answer: (C) Equilateral triangle

Q2. Medians of an Equilateral Triangle

In an equilateral triangle, all medians are:

(A) Equal in length
(B) Unequal in length
(C) Perpendicular to sides but unequal
(D) None of these

Answer: (A) Equal in length

Q3. Constructing an Altitude

To construct the altitude from vertex A to side BC (A not on BC) using compass and straightedge, the correct first step is to:

(A) Draw the circumcircle of triangle ABC.
(B) Draw the angle bisector of A.
(C) Draw the perpendicular bisector of BC.
(D) Draw an arc centred at A that intersects BC at two points.

Answer: (D) Draw an arc centred at A that intersects BC at two points.

Q4. Orthocentre of an Acute Triangle

In an acute-angled triangle, the orthocentre lies:

(A) Inside the triangle
(B) Outside the triangle
(C) On the triangle
(D) None of these

Answer: (A) Inside the triangle

Q5. Right-Angled Triangle

If one angle of a triangle is 90°, then the triangle is called:

(A) Right-angled triangle
(B) Acute triangle
(C) Obtuse triangle
(D) Equilateral triangle

Answer: (A) Right-angled triangle

Q6. Median of a Triangle

The line segment joining a vertex of a triangle to the midpoint of its opposite side is called:

(A) Altitude
(B) Median
(C) Perpendicular bisector
(D) Angle bisector

Answer: (B) Median

Q7. Altitude of a Triangle

In a triangle ABC, an altitude from vertex A is a line segment that:

(A) Joins A to the midpoint of BC
(B) Joins A to BC and is perpendicular to BC
(C) Joins A to BC and bisects A
(D) Joins A to the circumcentre of triangle ABC

Answer: (B) Joins A to BC and is perpendicular to BC

Q8. Scalene Triangle

The triangle having all three sides of different lengths is called:

(A) Scalene triangle
(B) Isosceles triangle
(C) Equilateral triangle
(D) Right triangle

Answer: (A) Scalene triangle

Q9. Angles of an Isosceles Triangle

In triangle ABC, AB = AC and B = 50°. What will be the measure of C?

(A) 40°
(B) 50°
(C) 80°
(D) 65°

Answer: (B) 50°

Q10. Constructing a Triangle

In constructing a triangle when two sides and an included angle are given, the first step is:

(A) Draw any side of the triangle
(B) Draw the included angle
(C) Draw a perpendicular bisector
(D) Measure the third side

Answer: (A) Draw any side of the triangle

Diagram-Based Questions

Q11. Find x

Given the angles of a triangle as (5x − 60)°, (2x + 40)°, and (3x − 80)°, find x.

(A) 28
(B) 30
(C) 25
(D) 45

Answer: (A) 28

Q12. Check for a Right Triangle

In triangle ABC, AB = 5 cm, BC = 12 cm, and AC = 13 cm. Is it a right triangle?

(A) Yes, right angle at A
(B) Yes, right angle at B
(C) Yes, right angle at C
(D) No

Answer: (B) Yes, right angle at B

Q13. Find the Third Angle

In triangle XYZ, if ∠X = 90° and ∠Y = 45°, what is the measure of ∠Z?

(A) 30°
(B) 45°
(C) 60°
(D) 90°

Answer: (B) 45°

Q14. Find x

In triangle ABC, AB = AC and BC and CD form a straight line. The exterior angle at C is 105°. Find x.

(A) 60°
(B) 65°
(C) 70°
(D) 75°

Answer: (D) 75°

Q15. Find the Unknown Angles

Find the unknown angles a and b, if l ∥ m.

Given:

• l ∥ m

• One angle is 40°.

• One angle at line m is 110°.

(A) a = 70° and b = 120°
(B) a = 70° and b = 110°
(C) a = 120° and b = 70°
(D) a = 60° and b = 110°

Answer: (B) a = 70° and b = 110°

Class 7 Maths Chapter 7 Important Questions PDF

For further practice, the Class 7 Maths Chapter 7 Important Questions PDF covers key topics such as triangle properties, angle calculations, medians, altitudes, orthocentres, and geometric constructions. Solve the questions independently and then check the answers to assess your understanding and identify areas that need more practice.

Why Choose Class 7 Maths Chapter 7 Important Questions by PW?

Class 7 Maths Chapter 7 Important Questions by PW provide practice across triangle properties, geometric constructions, angle relationships, and diagram-based problems.

• Recognise Triangle Types: Distinguish between equilateral, isosceles, scalene, acute, and right-angled triangles.

• Work with Medians: Understand how a median joins a vertex to the midpoint of the opposite side.

• Use Altitude Concepts: Identify perpendicular lines drawn from a vertex to the opposite side.

• Understand Orthocentres: Learn how the position of the orthocentre varies across different triangles.

• Find Missing Angles: Apply triangle angle properties to calculate unknown angles.

• Use Isosceles Properties: Apply the relationship between equal sides and their opposite angles.

• Practise Constructions: Strengthen understanding of triangle and altitude construction steps.

• Interpret Geometric Figures: Examine diagrams carefully and apply the relevant property to solve problems.

A Tale of Three Intersecting Lines develops your understanding of triangles through their sides, angles, medians, altitudes, and other important lines. The Class 7 Maths Chapter 7 Important Questions provide practice with these concepts through objective and diagram-based problems, helping you revise properties and apply them while solving geometry questions.

Related Resources

• CBSE Class 7 Maths Syllabus 

• CBSE Class 7 Maths NCERT Solutions

• CBSE Class 7 Maths Sample Papers

• CBSE Class 7 Maths Notes