Important Practice Problems for CBSE Class 7 Maths Chapter 6: The Triangle and Its Properties FREE PDF
Very Short Answer Type Questions:
Q1. Classify the following triangles according to their angles.
a) 75°, 45°, 60° → Acute angled triangle (all angles are less than 90°).
b) 90°, 30°, 60° → Right angled triangle (one angle is 90°).
c) 60°, 60°, 60° → Equilateral triangle (all angles are equal, each 60°).
d) 110°, 35°, 35° → Obtuse angled triangle (one angle is more than 90°).
Q2. Classify the following triangles according to their sides.
a) 7 cm, 5 cm, 6.5 cm → Scalene triangle (all sides are of different lengths).
b) 4 cm, 4 cm, 7 cm → Isosceles triangle (two sides are equal).
c) 3.8 cm, 4.9 cm, 3.8 cm → Isosceles triangle (two sides are equal).
d) 5.2 cm, 5.2 cm, 5.2 cm → Equilateral triangle (all sides are equal).
Q3. In an obtuse angled triangle, how many angles are obtuse?
Answer: 1 angle.
Q4. In an acute angled triangle, how many angles are acute?
Answer: 3 angles.
Q5. Write the names for:
1) The longest side of a right-angle triangle.
Answer: Hypotenuse.
2) The other name for the equilateral triangle.
Answer: Regular triangle.
Short Answers Type Questions:
Q6. One of the base angles in an isosceles triangle is 35°. Find the measure of the third angle.
Solution: In an isosceles triangle, the two base angles are equal. Let the third angle be x.
Base angle = 35° (two times).
Using the triangle angle sum property: 35° + 35° + x = 180°.
x = 180° - 70° = 110°.
Answer: 110°.
Q7. The three angles of a triangle are in the ratio of 6: 7: 5. Find the angles.
Solution: Let the angles be 6x , 7x , and 5x .
Sum of angles in a triangle = 180°.
6x + 7x + 5x = 180°.
18x = 180° → x = 10°.
Angles are 6x = 60°, 7x = 70°, and 5x = 50°.
Answer: 60°, 70°, 50°.
Q8. Is it possible to draw a triangle with sides?
a) 3 cm, 4 cm, 8 cm → No (sum of two smaller sides is not greater than the third side).
b) 4 cm, 6 cm, 10 cm → Yes (sum of any two sides is greater than the third side).
Q9. In a triangle ABC, which is the longest side if:
a) ∠A is a right angle
Answer: BC (opposite to the right angle).
b) ∠C is a right angle
Answer: AB (opposite to the right angle).
Q10. In a right-angled triangle, two acute angles are in the ratio of 4: 5. Find the acute angles of the triangle.
Solution: Let the acute angles be 4x and 5x.
Sum of acute angles in a right-angled triangle = 90°.
4x + 5x = 90°.
9x = 90° → x = 10°.
Acute angles are 4x = 40° and 5x = 50°.
Answer: 40°, 50°.
Long Answers Type Questions
Q11. In the following figure, ∠x: ∠y = 5: 3 and ∠ACD = 160°, find the values of x, y, and z.
Solution: Since ∠ACD is an exterior angle, ∠x + ∠y = 160°.
Let ∠x = 5k and ∠y = 3k.
5k + 3k = 160° → 8k = 160° → k = 20°.
∠x = 5k = 100°, ∠y = 3k = 60°.
∠z (third angle in triangle) = 180° (∠x + ∠y) = 20°.
Answer: 100°, 60°, 20°.
Q12. One of the exterior angles of a triangle is 80° and interior opposite angles are equal to each other. Find the measure of each of these two equal angles.
Solution: Let each interior opposite angle be x.
Sum of two opposite interior angles = exterior angle.
x + x = 80° → 2x = 80° → x = 40°.
Answer: 40°, 40°.
Q13. The length of the diagonal of a rectangular garden is 34 m. If its longer side measures 30 m, find the length of the shorter side of the garden.
Solution: Let the shorter side be x.
By the Pythagorean theorem: ${x^2} + {30^2} = {34^2}$.
${x^2} + 900 = 1156$.
${x^2} = 256$ → $x = 16$ m.
Answer: 16 m.
Q14. A ladder 10 m long is leaning against a wall. The foot of the ladder is 8 m away from the wall. Find the height up to which the ladder reaches the wall.
Solution: Let the height be h.
By the Pythagorean theorem: ${h^2} + {8^2} = {10^2}$.
${h^2} + 64 = 100$.
${h^2} = 36$ → $h = 6$ m.
Answer: 6 m.
Q15. In the given figure, find:
1) ∠ACD
2) ∠ADC
3) ∠DAE
Solution: Using the given angles in the figure:
∠ACD = 80°.
∠ADC = 150°.
∠DAE = 130°.
Answer: 80°, 150°, 130°.
5 Important Formulas of Class 7 Chapter 6 The Triangle and Its Properties You Shouldn’t Miss!
Understanding and remembering the key formulas in Chapter 6, "The Triangle and Its Properties," is essential for solving problems accurately. Here are five important formulas student should focus on:
1. Angle Sum Property of a Triangle
The sum of all interior angles of a triangle is always 180°.
$\angle A + \angle B + \angle C = 180° $
2. Exterior Angle Property
The measure of an exterior angle of a triangle is equal to the sum of the two opposite interior angles.
$\angle Exterior = \angle Opposite + \angle Opposite2$
3. Pythagorean Theorem (for Right-Angled Triangles)
In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
$c^2 = a^2 + b^2$
where $c$ is the hypotenuse, and $a$ and $b$ are the other two sides.
4. Perimeter of a Triangle
The perimeter of a triangle is the sum of the lengths of all its sides.
$\text{Perimeter} = a + b + c $
where $a$, $b$, and $c$ are the lengths of the three sides.
5. Area of a Right-Angled Triangle
The area of a right-angled triangle can be calculated using the base and height.
$\text{Area} = \frac{1}{2} \times \text{Base} \times \text{Height}$
Benefits of Important Questions for Class 7 Maths Chapter 6 The Triangle and Its Properties
Important questions for Class 7 Maths Chapter 6 help reinforce core concepts related to triangles, including types of triangles, properties, and angle sum properties.
By practising varied questions provided in the FREE PDF, students become better at applying different properties of triangles in problem-solving.
Going through key questions prepares students for exams by giving them an idea of question patterns and helping them practise thoroughly.
Important questions highlight the main topics to focus on, making revision efficient and targeted.
Regular practice enables students to solve questions faster, helping them manage their time well during exams.
Conclusion
Important questions for Class 7 Maths Chapter 6, "The Triangle and Its Properties," provide a valuable resource for students to strengthen their understanding, practise essential concepts, and prepare effectively for exams. By focusing on key topics and improving problem-solving skills, these questions help students approach their exams with confidence and a clear grasp of triangle properties. Regular practice with these questions enables efficient revision, ensuring a strong foundation in this chapter.
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FAQs on CBSE Class 7 Maths Important Questions Chapter 6 - The Triangle and Its Properties
1. What are the most important CBSE Class 7 questions on the angle sum property of a triangle (2025–26)?
- Expected question format: Given two angles of a triangle, calculate the third using angle sum property (Σ angles = 180°).
- Sample HOTS: If two angles of a triangle differ by 30° and their sum is 100°, what are all three angles?
- Exam tip: Always show working steps; marks are awarded for logical progression.
2. How can you identify different types of triangles in CBSE Class 7 important questions, based on side lengths and angles?
- Triangle by sides: Equilateral (all equal), Isosceles (exactly 2 equal), Scalene (none equal)
- Triangle by angles: Acute angled (all < 90°), Right angled (one 90°), Obtuse angled (one > 90°)
- Exam trend: Classification is a common 1-mark question; CBSE expects accurate terminology as per 2025–26 syllabus.
3. How do examiners set reasoning-based important questions on the exterior angle property for Class 7?
- Key property: An exterior angle equals the sum of the two remote (opposite) interior angles.
- Sample: If an exterior angle in ΔABC is 120° and one remote interior angle is 45°, find the other.
- Exam tip: Write the formula step and substitution to secure full marks.
4. What are high-weightage HOTS questions on the Pythagorean theorem for CBSE Class 7 maths?
- Application focus: Finding a missing side in a right-angled triangle when two sides are given (especially in real-life context, e.g., ladder, garden, field)
- Possible 3-mark HOTS: "A triangle has sides 6 cm, 8 cm, and 10 cm. Prove if it is a right-angled triangle. Show all calculations."
- Board trend: CBSE 2025–26 may mix conceptual and calculation elements.
5. Why are ‘impossible triangles’ featured in Class 7 important questions, and how are such problems solved?
- Exam logic: To test understanding of the triangle inequality: the sum of any two sides must be greater than the third side.
- Sample conceptual trap: "Can you have a triangle with sides 4 cm, 4 cm, 9 cm? Justify."
- Answer approach: Clearly check all pairs; if any fail, such a triangle cannot exist.
6. What marking schemes apply to ‘find the value of x’ angle-chasing questions in the CBSE Class 7 triangle properties chapter?
- Marking breakdown (2025–26): 1 mark: writing the property used, 1 mark: equation setup, 1 mark: correct working and answer.
- Common misconception: Missing property reference or skipping algebra steps may result in lost marks.
7. What are the frequently asked 2-mark important questions on ‘classification of triangles’ for CBSE Class 7?
- Types: Given three angles or three sides, classify the triangle both by sides and by angles.
- Expected answer: Two-part response: one for angle type, one for side type.
- Example: Angles 110°, 35°, 35° → Obtuse angled, isosceles triangle.
8. What pattern-based important questions can be expected on ratio of angles in triangles (Class 7, 2025–26)?
- Examiner's logic: Give ratios like 3:4:5 and ask students to find angle measures using x (e.g., 3x + 4x + 5x = 180° → x = 15°).
- Marking tip: Show set-up and substitution steps to gain all marks.
9. How do important questions test application of ‘triangle terminology’ such as hypotenuse, base, and regular triangle?
- Sample Q: What is the name of the longest side in a right-angled triangle? (Answer: Hypotenuse)
- Reason for testing: Reinforces language and identification, as required in new competency-based CBSE pattern.
10. What are some less obvious but important conceptual traps students face with Class 7 triangle questions in CBSE exams?
- Confusing angle and side properties: Assuming equal angles imply equal sides (only true in equilateral/isosceles, not all cases)
- Angle sum/exterior angle misapplication: Using the property for non-triangle shapes
- Missing units: Always label angle/length answers with correct units (degrees/cm)
11. What are some important questions for CBSE Class 7 on perimeter and area of right-angled triangles?
- Theme: Find perimeter using all side lengths; find area using Area = 1/2 × base × height
- Expected complexity: Often combined with Pythagoras to derive missing base/height first
12. How do important questions in CBSE Class 7 test understanding of base angles in isosceles triangles?
- Marking weightage: Typically 2-marks: one for identifying equal base angles, one for calculation of the third angle
- Exam trend: ‘If one base angle is 40°, find the vertex angle’ (use 180° sum)
13. What kinds of comparison questions appear in CBSE Class 7 triangle properties important questions?
- Sample comparison: Compare given triangles based on sides, angles, or properties (e.g., Which has a longer perimeter?)
- Marking focus: Clear reasoning and units; may require brief justification statement.
14. How can you spot higher-order thinking (HOTS) important questions related to triangle properties for CBSE 2025–26?
- Look for: Multi-step, real-life scenarios (e.g., ‘A tree is supported by two ropes forming a triangle with the ground. Calculate the length of one rope.’)
- Skill tested: Application of multiple properties (Pythagoras, exterior angle, perimeter, etc.) in one problem.
15. Why do CBSE Class 7 exams include questions asking to ‘justify’ or ‘explain’ whether a set of sides or angles can form a triangle?
- Exam intent: Tests reasoning and conceptual grasp, not just memorization
- How to answer: Quote triangle inequality or angle sum property explicitly in short justification for full marks.
