Last Updated on August 19, 2024 by XAM CONTENT
Hello students, we are providing case study questions for class 7 maths. Case study questions are the new question format that is introduced in CBSE board. The resources for case study questions are very less. So, to help students we have created chapterwise case study questions for class 7 maths. In this article, you will find case study questions for CBSE Class 7 Maths Chapter 6 Triangle and its Properties. It is a part of Case Study Questions for CBSE Class 7 Maths Series.
| Chapter | Triangle and its Properties |
| Type of Questions | Case Study Questions |
| Nature of Questions | Competency Based Questions |
| Board | CBSE |
| Class | 7 |
| Subject | Maths |
| Useful for | Class 7 Studying Students |
| Answers provided | Yes |
| Difficulty level | Mentioned |
| Important Link | Class 7 Maths Chapterwise Case Study |
Case Study Questions on Triangle and its Properties
Questions
Passage 1:
In a triangle first angle is 10° less than twice of second angle and third angle is 30° more than the second angle.
Q. 1. Find the sum of all first, second and third angle of triangle:
(a) 180°
(b) 70°
(c) 40°
(d) None of these
Difficulty Level: Easy
Ans. Option (a) is correct.
Explanation: We know that sum of all angles of triangle is 180°.
Q. 2. Which angle is smaller:
(a) First Angle
(b) Second Angle
(c) Third Angle
(d) Can’t Say
Difficulty Level: Easy
Ans. Option (b) is correct.
Explanation: Clearly given first and third both angles are greater than second angle (point to remember sum of any two sides of triangle is always greater than the third side)
Q. 3. Find the second angle:
(a) 70°
(b) 40°
(c) 90°
(d) 50°
Difficulty Level: Difficult
Ans. Option (b) is correct.
Explanation: let the second angle be x, then according to the question
first angle = 2x – 10°
third angle = second angle + 30°
third angle = x + 30°
as we know sum of all angles of triangle is 180°, therefore
first angle + second angle + third angle = 180°
(2x – 10) + (x) + (x + 30) = 180
4x + 20 = 180
4x = 180 – 20
4x = 160
x = 40°
hence required second angle = 40°
Q. 4. Find the first angle:
Difficulty Level: Difficult
Ans. 70°
Explanation: let the second angle be x, then according to the question
first angle = 2x – 10°
third angle = second angle + 30°
third angle = x + 30°
as we know sum of all angles of triangle is 180°, therefore
first angle + second angle + third angle = 180°
(2x – 10) + (x) + (x + 30) = 180
4x + 20 = 180
4x = 180 – 20
4x = 160
x = 160/4
x = 40°
first angle = 2x – 10
= 2(40) – 10
= 80 – 10
= 70°
Q. 5. Write the sum of supplementary angle of first angle and complementary angle of second angle:
Difficulty Level: Medium
Ans. 160°
Explanation: Here, supplementary angle
= 180° – (first angle)
= 180 – 70
= 110°
complementary angle = 90° – (second angle)
= 90 – 40
= 50°
Required Sum = 110 + 50 = 160°
Also check
- Visualizing Solid Shapes Class 7 Case Study Questions Maths Chapter 13
- Symmetry Class 7 Case Study Questions Maths Chapter 12
- Exponents and Powers Class 7 Case Study Questions Maths Chapter 11
- Algebraic Expressions Class 7 Case Study Questions Maths Chapter 10
- Perimeter and Area Class 7 Case Study Questions Maths Chapter 9
- Rational Numbers Class 7 Case Study Questions Maths Chapter 8
- Comparing Quantities Class 7 Case Study Questions Maths Chapter 7
- Triangle and its Properties Class 7 Case Study Questions Maths Chapter 6
- Lines and Angles Class 7 Case Study Questions Maths Chapter 5
- Simple Equations Class 7 Case Study Questions Maths Chapter 4
- Data Handling Class 7 Case Study Questions Maths Chapter 3
- Fractions and Decimals Class 7 Case Study Questions Maths Chapter 2
- Integers Class 7 Case Study Questions Maths Chapter 1
Topics from which case study questions may be asked
- Complementary Angles
- Supplementary Angles
- Intersecting Lines/Transversal
- Angles Made by a Transversal
- Transversal of Parallel Lines
- Medians of a triangle
- Altitudes of a triangle
- Exterior angle of a triangle
- Angle sum property of a triangle
- Sum of lengths of two sides of a triangle
- Pythagoras theorem
A triangle is a 3-sided closed figure formed by three line segments. The three sides and three angles of a triangle are the six elements
of the triangle.
On the basis of its sides, a triangle is equilateral, if all its 3 sides are equal; isosceles, if two of its sides are equal; scalene, if all sides are
unequal.
On the basis of the measure of its angles, a triangle is acute-angled, if all 3 angles are acute; right angled, if one of its angle is a right angle; obtuse angled, If one of its angles is obtuse.
Case study questions from the above given topic may be asked.
A triangle has 3 altitudes. In right angled triangle, two altitudes are two of its sides. Intersection point of three altitudes is called ORTHOCENTRE.
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Frequently Asked Questions (FAQs) on Triangle and its Properties Case Study
Q1: What is a triangle, and what are its basic properties?
A1: A triangle is a three-sided polygon with three angles. The sum of the angles in any triangle is always 180°. Triangles are classified based on their sides (scalene, isosceles, equilateral) and angles (acute, obtuse, right-angled).
Q2: What are the different types of triangles based on their sides?
A2: Triangles can be classified based on their sides as follows:
Scalene Triangle: All three sides are of different lengths.
Isosceles Triangle: Two sides are of equal length, and the third side is different.
Equilateral Triangle: All three sides are of equal length.
Q3: What are the different types of triangles based on their angles?
A3: Triangles can be classified based on their angles as follows:
Acute Triangle: All three angles are less than 90°.
Right-Angled Triangle: One of the angles is exactly 90°.
Obtuse Triangle: One of the angles is greater than 90°.
Q4: What is the Pythagoras theorem, and how is it related to triangles?
A4: The Pythagoras theorem applies to right-angled triangles and states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Q5: What is the significance of the triangle inequality property?
A5: The triangle inequality property states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. This property is essential in determining whether a given set of three lengths can form a triangle.
Q6: What is an exterior angle of a triangle, and what is its property?
A6: An exterior angle of a triangle is an angle formed by one side of the triangle and the extension of an adjacent side. The exterior angle property states that the measure of an exterior angle is equal to the sum of the two opposite interior angles.
Q7: What is the median of a triangle?
A7: A median of a triangle is a line segment drawn from a vertex to the midpoint of the opposite side. Every triangle has three medians, and they all intersect at a single point called the centroid, which is the triangle’s center of mass.
Q8: What is an altitude of a triangle?
A8: An altitude of a triangle is a perpendicular segment drawn from a vertex to the line containing the opposite side (or its extension). A triangle has three altitudes, and they intersect at a point called the orthocenter.
Q9: Are there any online resources or tools available for practicing comparing quantities case study questions?
A9: We provide case study questions for CBSE Class 8 Maths on our website. Students can visit the website and practice sufficient case study questions and prepare for their exams. If you need more case study questions, then you can visit Physics Gurukul website. they are having a large collection of case study questions for all classes.
