Practicing Class 7 Maths Chapter 7 A Tale of Three Intersecting Lines MCQs is one of the easiest ways to prepare for your CBSE Board school exams. This chapter introduces important geometry concepts such as triangles, collinear points, triangle construction, triangle inequality, medians, altitudes, and angle bisectors. Solving objective questions helps you understand these topics better and improves your confidence before the exam.
On this page, you will find carefully prepared MCQs based on the latest NCERT Ganita Prakash Part 1 syllabus. Each question comes with the correct answer and a simple explanation so that you can learn while practicing. These questions are useful for class tests, homework, periodic tests, and annual examinations.
If you want to practice more chapter-wise objective questions, explore our collection of Class 7 MCQs prepared according to the latest CBSE curriculum. Students who wish to strengthen their mathematics concepts can also visit our complete library of Class 7 Maths MCQs, where every chapter includes exam-focused practice questions with answers.
Read each question carefully, try to solve it on your own, and then check the explanation to understand the concept. Regular practice will help you improve your speed, accuracy, and problem-solving skills.
Class 7 Maths Chapter 7 A Tale of Three Intersecting Lines MCQs with Answers with Explanations
Practice these Class 7 Maths Chapter 7 A Tale of Three Intersecting Lines MCQs with Answers and explanations to test your understanding of the chapter and revise important concepts quickly. These NCERT-based multiple-choice questions cover topics like collinear points, triangle inequality, triangle construction, medians, altitudes, and angle bisectors. Solve each question on your own before checking the answer and explanation to strengthen your concepts and prepare confidently for your CBSE exams.
Q. Which set of points can form a triangle?
A. Three points lying on the same straight line
B. Three non-collinear points
C. Two points on a line and one overlapping point
D. Only points joined by curved lines
Answer:B
Explanation: A triangle is formed only when three points do not lie on the same straight line. Such points are called non-collinear points. They enclose a closed region with three sides. If all three points are collinear, they cannot form a triangle because no enclosed area is created.
Q. What happens when three vertices of a triangle lie on the same straight line?
A. A larger triangle is formed
B. An isosceles triangle is formed
C. No triangle can be formed
D. A right triangle is formed
Answer:C
Explanation: Observe the position of the three points carefully. When all the vertices lie on one straight line, the figure has no enclosed region. Since a triangle must be a closed shape with three sides, collinear points cannot make a triangle.
Q. Which condition must always be true for three line segments to form a triangle?
A. All three sides should be equal.
B. One side should be twice another side.
C. The sum of any two sides should be greater than the third side.
D. One angle should always be 90°.
Answer:C
Explanation: The triangle inequality is an important rule in geometry. It says that the total length of any two sides must always be greater than the remaining side. If this condition is not satisfied, the sides cannot meet to form a closed triangle.
Q. Can line segments of lengths 4 cm, 5 cm, and 10 cm form a triangle?
A. Yes, because all lengths are different.
B. Yes, because they have three sides.
C. No, because 4 + 5 is less than 10.
D. No, because one side is even.
Answer:C
Explanation: Before deciding, check the triangle inequality. Here, 4 cm + 5 cm = 9 cm, which is smaller than 10 cm. Since the sum of two sides is not greater than the third side, these line segments cannot form a triangle.
Q. What is the main use of a compass while constructing triangles?
A. To colour the figure
B. To draw circles and arcs with the required radius
C. To measure angles
D. To erase extra lines
Answer:B
Explanation: During triangle construction, a compass helps draw arcs and circles of fixed lengths. These arcs show possible locations of a vertex based on the given measurements. A ruler is then used to join the points and complete the required triangle accurately.
Q. What is a median of a triangle?
A. A line joining two midpoints
B. A line from a vertex to the midpoint of the opposite side
C. A line joining two angles
D. A line outside the triangle
Answer:B
Explanation: A median starts from a vertex and ends at the midpoint of the opposite side. Every triangle has three medians, and all of them meet at a single point called the centroid. Medians help divide a triangle into smaller regions of equal area.
Q. The point where the three medians of a triangle meet is called the:
A. Orthocenter
B. Incenter
C. Centroid
D. Circumcenter
Answer:C
Explanation: Think about the special lines inside a triangle. When all three medians intersect, they meet at the centroid. This point is often called the balancing point because a triangular sheet can balance at this location.
Q. Which statement correctly describes an altitude of a triangle?
A. It always joins two vertices.
B. It divides an angle into two equal parts.
C. It is drawn from a vertex perpendicular to the opposite side.
D. It joins the midpoints of two sides.
Answer:C
Explanation: An altitude is identified by its right angle. It begins at a vertex and meets the opposite side at 90°. Every triangle has three altitudes, and they intersect at a point known as the orthocenter.
Q. The common meeting point of the three altitudes of a triangle is known as the:
A. Centroid
B. Incenter
C. Orthocenter
D. Midpoint
Answer:C
Explanation: Different special lines in a triangle meet at different points. The three altitudes always intersect at the orthocenter. Its position depends on the type of triangle, but it is always formed by the meeting of the altitudes.
Q. What does an angle bisector do in a triangle?
A. It divides a side into two equal parts.
B. It divides an angle into two equal angles.
C. It creates two different triangles of unequal area.
D. It joins the midpoint of two sides.
Answer:B
Explanation: An angle bisector splits one angle into two equal angles. Each triangle has three angle bisectors, and they meet at the incenter. The incenter is equally distant from all three sides of the triangle, making it an important point in geometry.
Q. Which point is formed by the intersection of the three angle bisectors of a triangle?
A. Orthocenter
B. Centroid
C. Incenter
D. Midpoint
Answer:C
Explanation: Every angle bisector divides a vertex angle into two equal parts. When all three angle bisectors are drawn, they meet at a single point called the incenter. This point is always inside the triangle and is at an equal distance from all three sides.
Q. Which instrument is mainly used to measure the length of a line segment while constructing a triangle?
A. Compass
B. Protractor
C. Ruler
D. Divider
Answer:C
Explanation: A ruler helps measure and draw line segments of the required length. During triangle construction, the ruler is used along with a compass. The ruler draws straight sides, while the compass creates arcs needed to locate the third vertex.
Q. Which of the following sets of side lengths can form a triangle?
A. 5 cm, 6 cm, 10 cm
B. 3 cm, 4 cm, 8 cm
C. 2 cm, 5 cm, 8 cm
D. 4 cm, 6 cm, 12 cm
Answer:A
Explanation: Apply the triangle inequality rule to each option. For 5 cm, 6 cm, and 10 cm, the sum of the two smaller sides is 11 cm, which is greater than 10 cm. Therefore, these three sides can be joined to make a triangle.
Q. Which statement about a triangle is always correct?
A. It has two sides and three angles.
B. It is formed using three non-collinear points.
C. It always has four vertices.
D. It must contain one right angle.
Answer:B
Explanation: A triangle is the simplest closed polygon made by joining three non-collinear points. It always has three sides, three vertices, and three angles. The angles may vary, so a right angle is not necessary in every triangle.
Q. Why is the triangle inequality theorem important?
A. It helps identify equal angles only.
B. It decides whether three given lengths can form a triangle.
C. It measures the perimeter directly.
D. It tells the colour of the triangle.
Answer:B
Explanation: Before constructing a triangle, we first check whether the given side lengths satisfy the triangle inequality. This saves time and ensures that the three line segments can actually meet to form a closed figure.
Q. A triangle has sides of 8 cm, 7 cm, and 5 cm. What can you say about it?
A. It cannot be formed.
B. It satisfies the triangle inequality.
C. Two sides are too short to meet.
D. It is not a closed figure.
Answer:B
Explanation: Check each pair of sides. Here, 8 + 7 > 5, 8 + 5 > 7, and 7 + 5 > 8. Since all three conditions are satisfied, the given side lengths can form a triangle successfully.
Q. Which special line joins a vertex to the midpoint of the opposite side?
A. Altitude
B. Angle bisector
C. Median
D. Perpendicular bisector
Answer:C
Explanation: A median starts at a vertex and ends exactly at the midpoint of the opposite side. It is different from an altitude because it does not have to be perpendicular. Every triangle contains three medians meeting at the centroid.
Q. Which statement about the centroid is correct?
A. It is formed by the angle bisectors.
B. It is the meeting point of the medians.
C. It is outside every triangle.
D. It is formed by the altitudes.
Answer:B
Explanation: Imagine drawing all three medians of a triangle. They always intersect at one point called the centroid. This point divides each median in a fixed ratio and is often referred to as the balancing point of a triangle.
Q. What is the angle between an altitude and the opposite side?
A. 30°
B. 45°
C. 60°
D. 90°
Answer:D
Explanation: The word "altitude" itself suggests height. An altitude is drawn from a vertex to the opposite side so that it makes a right angle. Therefore, the angle formed is always 90°, making the altitude perpendicular to the side.
Q. Which of the following is not a special line inside a triangle?
A. Median
B. Angle bisector
C. Altitude
D. Radius
Answer:D
Explanation: Medians, altitudes, and angle bisectors are important lines studied inside triangles because each has a specific construction and point of intersection. A radius, however, is related to circles, not triangles, so it is not considered a special line of a triangle.
Q. Which of the following best describes a collinear set of points?
A. Points that form a closed figure
B. Points that lie on the same straight line
C. Points that are equally spaced
D. Points joined by curved lines
Answer:B
Explanation: Collinear points are points that lie on a single straight line. Since they do not enclose any region, they cannot form a triangle. Identifying whether points are collinear or non-collinear is one of the first steps in understanding triangle formation.
Q. What is the first thing you should check before deciding whether three given lengths can form a triangle?
A. Whether all sides are equal
B. Whether one side is horizontal
C. Whether the triangle inequality is satisfied
D. Whether all angles are equal
Answer:C
Explanation: Before drawing or constructing a triangle, always verify the triangle inequality. If the sum of any two sides is greater than the third side, the triangle can be formed. This simple check helps avoid incorrect constructions.
Q. Which pair of tools is commonly used to construct a triangle in geometry?
A. Pencil and eraser
B. Compass and ruler
C. Divider and calculator
D. Scale and colour pencils
Answer:B
Explanation: Triangle construction requires accuracy. A ruler is used to draw straight line segments, while a compass helps draw arcs with the required radius. Together, these tools make it possible to construct triangles based on the given measurements.
Q. Which statement about an angle bisector is correct?
A. It always passes through the midpoint of a side.
B. It divides an angle into two equal parts.
C. It is always perpendicular to the opposite side.
D. It joins two vertices of a triangle.
Answer:B
Explanation: An angle bisector is drawn from a vertex and splits that angle into two equal angles. It is different from a median or an altitude because its purpose is to divide the angle, not the side or the height of the triangle.
Q. What is the main purpose of drawing a median in a triangle?
A. To divide an angle into two equal parts
B. To join a vertex with the midpoint of the opposite side
C. To measure the perimeter
D. To construct a circle inside the triangle
Answer:B
Explanation: A median connects a vertex to the midpoint of the opposite side. It helps divide the triangle into two regions of equal area. Understanding medians also makes it easier to identify the centroid, where all three medians meet.
Q. If the lengths of two sides of a triangle are 6 cm and 9 cm, which of the following can be the third side?
A. 16 cm
B. 15 cm
C. 4 cm
D. 3 cm
Answer:C
Explanation: The third side must be greater than the difference of the other two sides and smaller than their sum. Here, it should be greater than 3 cm and less than 15 cm. Among the given options, only 4 cm satisfies both conditions.
Q. Which point is often called the balancing point of a triangle?
A. Incenter
B. Orthocenter
C. Centroid
D. Vertex
Answer:C
Explanation: If you cut out a triangle from cardboard, it can balance at the centroid. This point is formed where the three medians intersect. It is an interesting practical application that helps students understand the importance of the centroid.
Q. Which statement correctly compares a median and an altitude?
A. Both always divide an angle into two equal parts.
B. A median joins a vertex to the midpoint, while an altitude is perpendicular to the opposite side.
C. Both always meet outside the triangle.
D. They are two different names for the same line.
Answer:B
Explanation: Although both lines start from a vertex, they serve different purposes. A median reaches the midpoint of the opposite side, whereas an altitude is drawn at a right angle to the opposite side. Remembering this difference helps avoid common mistakes.
Q. Why are non-collinear points necessary for forming a triangle?
A. They create a closed figure with three sides.
B. They always make equal angles.
C. They produce four sides.
D. They keep all sides equal.
Answer:A
Explanation: A triangle must enclose an area. This is possible only when the three points are not on the same straight line. Non-collinear points allow the sides to meet and form a closed geometric figure called a triangle.
Q. A student draws all three medians, all three altitudes, and all three angle bisectors of a triangle. How many different special intersection points are formed?
A. One
B. Two
C. Three
D. Six
Answer:C
Explanation: Each group of special lines has its own point of intersection. The medians meet at the centroid, the altitudes meet at the orthocenter, and the angle bisectors meet at the incenter. Together, these form three important points studied in this chapter.
Why Practice Class 7 Maths Chapter 7 A Tale of Three Intersecting Lines MCQs?
Practicing these MCQs is a smart way to revise the chapter without spending too much time reading the complete textbook again. Objective questions help you quickly test your understanding and find the topics that need more practice.
These questions are based on NCERT concepts and follow the latest CBSE pattern. They help you prepare for classroom quizzes, unit tests, periodic assessments, half-yearly exams, and annual examinations.
By solving these MCQs regularly, you can:
- Revise important concepts in less time.
- Improve your accuracy in objective questions.
- Build confidence before school exams.
- Understand where you make mistakes.
- Strengthen your basic geometry concepts.
- Practice questions similar to those asked in CBSE assessments.
Regular practice also improves logical thinking and helps you answer questions more confidently during examinations.
Topics Covered in Chapter 7
This chapter helps students understand the basics of triangles and the important lines inside them. While solving the MCQs, you will revise the following concepts:
- Collinear and non-collinear points
- Formation of a triangle
- Triangle inequality theorem
- Construction of triangles using given measurements
- Types of triangles
- Median of a triangle
- Altitude of a triangle
- Angle bisector
- Centroid
- Orthocenter
- Incenter
- Basic properties of triangles
Understanding these concepts makes it easier to solve both objective and descriptive questions in your exams.
Tips to Score Better in Class 7 Maths Chapter 7 MCQs
Scoring well in geometry becomes easier when your concepts are clear. These simple tips can help you perform better in exams.
- Read every question carefully before selecting an answer.
- Draw a rough figure whenever a question involves triangles.
- Remember that three collinear points cannot form a triangle.
- Learn the triangle inequality theorem with examples.
- Do not confuse medians, altitudes, and angle bisectors.
- Practice NCERT questions before attempting extra MCQs.
- Revise important diagrams regularly.
- Check the explanations for every incorrect answer and understand your mistake.
- A few minutes of daily practice can make a big difference in your exam preparation.
