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CBSE Class 7 Mathematics Chapter 7 A Tale of Three Intersecting Lines Worksheet with Answers

Chapter 7 'A Tale of Three Intersecting Lines' introduces students to the fascinating geometry of triangles — shapes formed when three non-collinear points are joined by straight lines. This worksheet systematically tests understanding of triangle classification by sides and angles, the fundamental angle sum property, exterior angle theorem, and triangle inequality conditions. Designed for CBSE Class 7 students following the NCERT curriculum, it provides structured practice to build confidence before school assessments.

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Key takeaways

  • ✓Complete worksheet covering triangle types, angle sum property (180°), exterior angle property, and triangle inequality from NCERT Class 7 Mathematics Chapter 7
  • ✓30+ graded questions across MCQs, fill-in-the-blanks, true/false, short-answer, long-answer and one real-world case study
  • ✓Suggested time: 60 minutes; Difficulty: Easy to Moderate with HOTS questions for advanced learners
  • ✓Full answer key with brief explanations for every question to support self-assessment and concept revision
  • ✓Aligns perfectly with 2025 CBSE Class 7 Mathematics syllabus and NCERT textbook terminology
  • ✓Printable A4 format suitable for home practice, classroom tests, and quick revision before examinations

Worksheet Details and Instructions

This worksheet is designed for 60 minutes of focused practice and is suitable for students who have completed reading NCERT Class 7 Mathematics Chapter 7. The difficulty level is Easy to Moderate, with a few Higher Order Thinking Skills (HOTS) questions in Section E to challenge advanced learners. Students should attempt the worksheet with a pencil, ruler, and eraser. Diagrams should be drawn neatly where required. Calculators are not necessary as all calculations involve basic arithmetic. Teachers can use this as a formative assessment tool, while students can use it for self-study and exam preparation. Each section targets specific question types commonly found in CBSE examinations, ensuring comprehensive coverage of the chapter.
  • Total Marks: 50 | Suggested Time: 60 minutes
  • Difficulty Level: Easy to Moderate with HOTS elements
  • Materials needed: Pencil, ruler, eraser, protractor (optional)
  • Attempt all sections sequentially for best learning outcome
  • Refer to the answer key only after completing your attempt

Quick Chapter Recap: A Tale of Three Intersecting Lines

Chapter 7 explores triangles and their properties systematically. A triangle is a closed figure formed by three line segments joining three non-collinear points. Triangles can be classified by their sides into equilateral (all three sides equal), isosceles (two sides equal), and scalene (all sides different). By angles, they are classified as acute-angled (all angles less than 90°), right-angled (one angle exactly 90°), and obtuse-angled (one angle greater than 90°). The Angle Sum Property states that the sum of the three interior angles of any triangle is always 180°. The Exterior Angle Property tells us that an exterior angle of a triangle equals the sum of the two interior opposite angles. Finally, the Triangle Inequality Property states that the sum of any two sides of a triangle must always be greater than the third side. These foundational concepts form the basis for advanced geometry in higher classes.
  • Triangle: A closed figure made by three line segments joining three non-collinear points
  • Classification by sides: Equilateral, Isosceles, Scalene
  • Classification by angles: Acute-angled, Right-angled, Obtuse-angled
  • Angle Sum Property: Sum of three interior angles = 180°
  • Exterior Angle Property: Exterior angle = Sum of two interior opposite angles
  • Triangle Inequality: Sum of any two sides > third side

Section A: Multiple Choice Questions (1 mark each)

This section contains six multiple-choice questions testing fundamental concepts from Chapter 7. Each question has four options, and only one is correct. These questions assess your understanding of triangle classification, angle sum property, exterior angles, and triangle inequality. Read each question carefully, eliminate obviously wrong options, and choose the most appropriate answer. Mark your answer clearly. MCQs are a staple of CBSE examinations and require both conceptual clarity and careful reading to avoid common traps.
  • Q1. The sum of the three interior angles of a triangle is: (a) 90° (b) 180° (c) 270° (d) 360°
  • Q2. A triangle with all sides of different lengths is called: (a) Equilateral (b) Isosceles (c) Scalene (d) Right-angled
  • Q3. A triangle with one angle equal to 90° is: (a) Acute-angled (b) Right-angled (c) Obtuse-angled (d) Equilateral
  • Q4. If two angles of a triangle are 45° and 55°, the third angle is: (a) 70° (b) 80° (c) 90° (d) 100°
  • Q5. An exterior angle of a triangle is equal to: (a) One interior angle (b) Sum of all three interior angles (c) Sum of two interior opposite angles (d) Difference of two interior angles
  • Q6. Which of the following can be the sides of a triangle? (a) 2 cm, 3 cm, 6 cm (b) 4 cm, 5 cm, 9 cm (c) 5 cm, 6 cm, 10 cm (d) 3 cm, 4 cm, 8 cm

Section B: Fill in the Blanks (1 mark each)

This section tests recall and understanding through completion-type questions. Write the correct word, number, or term in each blank. Answers should be precise and match NCERT terminology exactly. Pay attention to units where applicable. These questions often appear in CBSE Class 7 Mathematics examinations and require you to remember key definitions, properties, and numerical relationships from the chapter. Review your NCERT Class 7 Mathematics textbook if you are uncertain about any concept.
  • Q7. A triangle with all three sides equal is called an __________ triangle.
  • Q8. The sum of the lengths of any two sides of a triangle is always __________ than the third side.
  • Q9. In a right-angled triangle, the angle opposite to the hypotenuse is __________.
  • Q10. A triangle having all angles less than 90° is called an __________ triangle.
  • Q11. The exterior angle of a triangle is equal to the sum of the two __________ opposite angles.
  • Q12. A triangle with two equal sides is known as an __________ triangle.

Section C: True or False (1 mark each)

Carefully read each statement and decide whether it is true or false. Write 'True' or 'False' next to each question number. Some statements may seem correct at first glance but contain subtle errors, so read attentively. This section evaluates your ability to distinguish between correct and incorrect mathematical statements related to triangle properties, a skill frequently tested in CBSE examinations. If a statement is false, you may write the correct version in the margin for your own revision, though it is not required for marking.
  • Q13. Every equilateral triangle is also an isosceles triangle.
  • Q14. A triangle can have two right angles.
  • Q15. The exterior angle of a triangle is always greater than each of the interior opposite angles.
  • Q16. A triangle can have sides of lengths 3 cm, 4 cm, and 8 cm.
  • Q17. The sum of any two angles of a triangle is always less than 180°.
  • Q18. An obtuse-angled triangle has one angle greater than 90°.

Section D: Short Answer Questions (2 marks each)

Answer the following questions in 2 to 3 sentences or show the required calculation steps clearly. Each question carries 2 marks. Marks are awarded for method as well as the final answer, so always write the formula or property you are using. Diagrams should be neat and labelled. This section appears regularly in CBSE Class 7 Mathematics exams and tests your ability to apply concepts such as angle sum property and triangle inequality in straightforward problem-solving contexts. Show all working to earn full credit even if the final answer has a minor error.
  • Q19. In triangle ABC, angle A = 50° and angle B = 70°. Find angle C.
  • Q20. Can a triangle have angles 60°, 70°, and 60°? Justify your answer using the angle sum property.
  • Q21. The exterior angle at vertex C of triangle ABC is 120°. If one of the interior opposite angles is 50°, find the other interior opposite angle.
  • Q22. Check whether sides of lengths 7 cm, 24 cm, and 25 cm can form a triangle. Use the triangle inequality property.
  • Q23. In an isosceles triangle, the equal angles are each 55°. Find the third angle.

Section E: Long Answer and HOTS Questions (3 marks each)

These questions require detailed solutions, logical reasoning, and sometimes multi-step problem solving. Write clear explanations, draw diagrams where necessary, and state the properties or theorems you are applying. HOTS (Higher Order Thinking Skills) questions test your ability to synthesize multiple concepts from NCERT Class 7 Mathematics Chapter 7. Allocate sufficient time to these questions. Full marks are awarded only when the method, reasoning, and final answer are all correct. These mirror the kind of application-based and analytical questions increasingly favoured in CBSE examinations.
  • Q24. In triangle PQR, angle P = 3x, angle Q = 2x, and angle R = x. Find the value of x and all three angles. Also state what type of triangle PQR is by its angles.
  • Q25. One angle of a triangle is 80° and the other two angles are equal. Find the measure of each of the equal angles. Classify the triangle by its angles.
  • Q26. The sides of a triangle are in the ratio 3:4:5. If the perimeter of the triangle is 36 cm, find the length of each side. Verify using the triangle inequality property.

Section F: Case-Study Based Question (4 marks)

Read the scenario carefully and answer the sub-questions that follow. Case-study questions are now a standard feature in CBSE Class 7 Mathematics examinations and test your ability to apply chapter concepts to real-life or practical situations. This question integrates multiple ideas from Chapter 7 including triangle classification, angle sum property, and triangle inequality. Answer all parts; marks are distributed across sub-questions. Write neatly and show calculations where required. Such questions help bridge the gap between theoretical knowledge and everyday problem-solving.

Complete Answer Key with Explanations

Below is the full answer key for all sections of this worksheet. Each answer includes a brief explanation or the property used, enabling students to self-assess and understand mistakes. Cross-check your answers only after completing the entire worksheet. If you scored below 70 per cent, revisit the relevant sections in your NCERT Class 7 Mathematics textbook and reattempt the questions. Consistent practice with worksheets like this one significantly improves performance in CBSE school exams and builds a strong foundation for higher classes.
  • Section A Answers: Q1.(b) 180° [Angle Sum Property] | Q2.(c) Scalene | Q3.(b) Right-angled | Q4.(b) 80° [180° – 45° – 55° = 80°] | Q5.(c) Sum of two interior opposite angles [Exterior Angle Property] | Q6.(c) 5, 6, 10 [5+6=11>10; 6+10=16>5; 5+10=15>6, all satisfied]
  • Section B Answers: Q7. equilateral | Q8. greater | Q9. 90° | Q10. acute-angled | Q11. interior | Q12. isosceles
  • Section C Answers: Q13. True [Every equilateral has two equal sides, hence isosceles] | Q14. False [Sum would exceed 180°] | Q15. True [Exterior angle = sum of two opposite interior angles, so greater than each] | Q16. False [3+4=7<8, violates triangle inequality] | Q17. True [If sum were ≥180°, third angle would be ≤0°] | Q18. True
  • Section D Answers: Q19. 60° | Q20. No, sum = 190° ≠ 180° | Q21. 70° [120° – 50° = 70°] | Q22. Yes; 7+24=31>25, 24+25=49>7, 7+25=32>24, all satisfied | Q23. 70° [Let third angle = x; 55°+55°+x=180°, x=70°]
  • Section E Answers: Q24. x=30°; angles 90°, 60°, 30°; right-angled triangle | Q25. Each equal angle = 50°; 80°+50°+50°=180°; acute-angled triangle | Q26. Sides 9 cm, 12 cm, 15 cm [ratio 3:4:5, sum=36]; verification: 9+12=21>15, 12+15=27>9, 9+15=24>12, all hold
  • Section F Answers: (i) angle C = 180° – 55° – 65° = 60° | (ii) Acute-angled triangle (all angles < 90°) | (iii) 12+15=27>18 ✓; 15+18=33>12 ✓; 12+18=30>15 ✓; all conditions satisfied, valid triangle

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Tips for Scoring Full Marks in Triangle Geometry

Success in CBSE Class 7 Mathematics Chapter 7 requires both conceptual clarity and disciplined practice. Always draw neat, labelled diagrams even if the question does not explicitly ask for one; examiners appreciate visual reasoning. When applying the angle sum property, write the equation clearly: angle A + angle B + angle C = 180°. For triangle inequality, check all three combinations of sides, not just one. Memorize the classification of triangles by both sides and angles, as mix-up between acute, obtuse, and right-angled is a common error. Practice at least 20 to 25 problems from NCERT exercises and supplementary worksheets like this one. Revise the properties daily for a week before the exam. Time yourself during practice to build speed. Review your errors immediately and note down tricky questions in a separate notebook for quick revision.
  • Draw and label all diagrams neatly; use a ruler and sharp pencil
  • State the property or theorem you are using before applying it
  • For triangle inequality, verify all three pairs of sides
  • Do not confuse classification by sides (equilateral, isosceles, scalene) with classification by angles
  • Attempt NCERT in-text and end-of-chapter exercises at least twice
  • Use worksheets like this one for timed practice and self-assessment

Common Mistakes Students Make in Chapter 7

Many Class 7 students incorrectly assume that if two sides of a triangle are given, the third side can be any positive number; they forget to apply the triangle inequality property. Another frequent error is adding only two angles and forgetting the third when using the angle sum property, leading to incomplete answers. Students often confuse the exterior angle property, mistakenly subtracting instead of adding the two interior opposite angles. Misclassification of triangles is common: for instance, calling a triangle with angles 50°, 60°, 70° as 'isosceles' instead of 'acute-angled scalene'. During exams, many skip drawing diagrams to save time, which increases the chance of conceptual errors. Finally, students sometimes write the final answer without units (degrees for angles, cm for sides), losing easy marks. Awareness of these pitfalls and deliberate practice can eliminate most errors.
  • Forgetting to check all three triangle inequality conditions
  • Incomplete application of angle sum property (missing the third angle)
  • Confusing exterior angle property formula or operation
  • Mixing up classification by sides versus classification by angles
  • Skipping diagram drawing, leading to visualization errors
  • Omitting units in final answers (degrees, centimetres)

Frequently asked questions

What is the angle sum property of a triangle?+
The angle sum property states that the sum of all three interior angles of any triangle is always exactly 180 degrees, regardless of the triangle's shape or size.
How do I classify a triangle by its sides?+
Triangles are classified by sides as equilateral (all three sides equal), isosceles (exactly two sides equal), or scalene (all three sides of different lengths).
What is the exterior angle property?+
The exterior angle of a triangle is equal to the sum of the two interior opposite angles. For example, if an exterior angle is 100° and one opposite interior angle is 40°, the other is 60°.
How does the triangle inequality property work?+
The triangle inequality states that the sum of the lengths of any two sides of a triangle must be strictly greater than the length of the third side. This must hold for all three combinations.
Can a triangle have two obtuse angles?+
No. If a triangle had two obtuse angles (each greater than 90°), their sum alone would exceed 180°, violating the angle sum property. A triangle can have at most one obtuse angle.
Is every equilateral triangle also isosceles?+
Yes. An equilateral triangle has all three sides equal, which means at least two sides are equal, satisfying the definition of an isosceles triangle as well.
What type of triangle has angles 90°, 45°, and 45°?+
This triangle is classified as a right-angled triangle (because one angle is 90°) and also an isosceles triangle (because the two angles opposite the equal sides are 45° each).
How many questions on triangles appear in CBSE Class 7 Maths exams?+
Typically, CBSE Class 7 Mathematics exams include 3 to 5 questions from Chapter 7, ranging from 1-mark MCQs and fill-in-the-blanks to 3-mark application problems, totaling around 8 to 12 marks.
Where can I find more practice worksheets for Class 7 Maths Chapter 7?+
NCERT exemplar problems, CBSE sample papers, and online platforms like CBSETUTOR.ai offer chapter-wise worksheets, mock tests, and instant doubt-solving for comprehensive practice and revision.
Why is drawing a diagram important in triangle problems?+
A neat, labelled diagram helps visualize the given information, prevents calculation errors, and often reveals relationships between angles and sides that are not obvious from the text alone, earning you method marks even if the final answer is wrong.

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