Basic Geometric Concepts - Problems on Triangles - Problem Set MCQ & Objective Questions
Understanding basic geometric concepts, particularly problems on triangles, is crucial for students preparing for school and competitive exams. Practicing MCQs and objective questions enhances your problem-solving skills and boosts your confidence. Engaging with practice questions helps you identify important concepts and improves your chances of scoring better in exams.
What You Will Practise Here
Types of triangles: scalene, isosceles, and equilateral
Properties of triangles, including angles and sides
Triangle inequality theorem and its applications
Area and perimeter calculations for different triangles
Congruence criteria: SSS, SAS, ASA, AAS, and RHS
Basic theorems related to triangles, such as Pythagorean theorem
Diagrams and visual representations to enhance understanding
Exam Relevance
Basic geometric concepts, especially problems on triangles, are frequently tested in CBSE, State Boards, NEET, and JEE examinations. Students can expect questions that assess their understanding of triangle properties, calculations of area and perimeter, and the application of congruence criteria. Common question patterns include multiple-choice questions that require both conceptual knowledge and practical application.
Common Mistakes Students Make
Confusing the properties of different types of triangles
Misapplying the triangle inequality theorem
Forgetting to check for congruence criteria in problem-solving
Errors in calculating area and perimeter due to incorrect formula usage
FAQs
Question: What are the key properties of an equilateral triangle? Answer: An equilateral triangle has all three sides equal and all angles measuring 60 degrees.
Question: How do I calculate the area of a triangle? Answer: The area can be calculated using the formula: Area = 1/2 × base × height.
Now is the time to strengthen your understanding of triangles! Dive into our practice MCQs and test your knowledge to excel in your exams. Remember, consistent practice is the key to success!
Q. If a triangle has sides of lengths 7 cm, 24 cm, and 25 cm, what type of triangle is it?
A.
Equilateral
B.
Isosceles
C.
Scalene
D.
Right
Solution
This triangle is a right triangle because 7² + 24² = 25² (49 + 576 = 625).
Q. If the lengths of two sides of a triangle are 5 cm and 12 cm, what is the range of possible lengths for the third side?
A.
1 cm to 17 cm
B.
6 cm to 16 cm
C.
7 cm to 12 cm
D.
5 cm to 12 cm
Solution
The length of the third side must be greater than the difference of the other two sides and less than their sum: |5 - 12| < third side < 5 + 12, which gives 7 cm < third side < 17 cm.
Q. If the lengths of two sides of a triangle are 5 cm and 7 cm, what is the range of possible lengths for the third side?
A.
2 cm to 12 cm
B.
3 cm to 11 cm
C.
4 cm to 10 cm
D.
5 cm to 9 cm
Solution
The length of the third side must be greater than the difference of the other two sides and less than their sum: |5 - 7| < third side < 5 + 7, which gives 2 < third side < 12.
Q. If the lengths of two sides of a triangle are 6 cm and 8 cm, what is the range of possible lengths for the third side?
A.
2 cm to 14 cm
B.
2 cm to 10 cm
C.
2 cm to 12 cm
D.
2 cm to 8 cm
Solution
The length of the third side must be greater than the difference of the other two sides and less than their sum: |6 - 8| < third side < 6 + 8, which gives 2 cm < third side < 14 cm.