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.
Important Study Materials for Class 7 Maths Chapter 6
CBSE Class 7 Maths Important Questions for All Chapters
Class 7 Maths Important Questions and Answers cover key topics, aiding in thorough preparation and making revision simpler.
Important Study Materials for Class 7 Maths
FAQs on CBSE Class 7 Maths Important Questions Chapter 6 - The Triangle and Its Properties
1. What are important questions for the chapter "The Triangle and Its Properties"?
Important questions cover the main concepts of the chapter, such as types of triangles, angle sum property, exterior angle property, and the Pythagorean theorem. They help students focus on essential topics.
2. How do important questions help in preparing for exams?
Important questions allow students to practise key topics and understand the types of questions that might appear in exams, boosting their confidence and preparation.
3. What is the angle sum property of a triangle?
The angle sum property states that the sum of all interior angles of a triangle is always 180 degrees.
4. Why is it important to learn the exterior angle property?
The exterior angle property helps in solving problems related to angles in triangles by connecting the exterior angle with the opposite interior angles, a commonly tested concept.
5. Are the Important Questions for Chapter 6 FREE PDF enough to understand this chapter?
Yes, practising important questions provides a solid understanding, but it is also helpful to review the textbook examples and exercises for comprehensive knowledge.
6. What are the different types of triangles explained in this chapter?
This chapter covers types of triangles based on sides (equilateral, isosceles, and scalene) and angles (acute, right, and obtuse).
7. How is the Pythagorean theorem used in this chapter?
The Pythagorean theorem is used in right-angled triangles to relate the lengths of sides, helping students solve problems involving side measurements.
8. What kind of questions can I expect from this chapter in exams?
You can expect questions on calculating angles, identifying triangle types, applying the angle sum and exterior angle properties, and using the Pythagorean theorem in right-angled triangles.
9. How often should I practise these important questions?
Regular practice, like once a week, is recommended to keep the concepts fresh and build confidence in problem-solving.
10. Can I use these questions for quick revision?
Yes, these important questions are ideal for a quick revision before exams, as they cover all essential topics of the chapter.
11. Why is it important to learn about triangles in Class 7 Maths?
Learning about triangles builds a foundation for geometry, which is useful in higher classes and helps develop spatial understanding and reasoning.
12. How does solving these questions improve my understanding of geometry?
Solving these questions sharpens your knowledge of triangle properties, making it easier to understand more complex geometry topics in future classes.
13. What resources can help alongside important questions for this chapter?
Apart from important questions, the CBSE textbook, NCERT Solutions Vedantu’s free PDFs, and video tutorials can provide additional help to reinforce understanding.
