Important Questions Maths Chapter 7 Class 7 Ganit Prakash

A Tale of Three Intersecting Lines

1. What is a triangle?

Ans: A triangle is a closed figure with three sides and three angles formed by joining three non-collinear points.

2. What is an equilateral triangle?

Ans: A triangle in which all three sides are equal in length is called an equilateral triangle.

3. How can we construct an equilateral triangle using a compass?

Ans: Draw a base, then use a compass to draw arcs of equal radius from each endpoint. The intersection gives the third vertex.

4. What is an isosceles triangle?

Ans: A triangle with two equal sides is called an isosceles triangle.

5. What is a scalene triangle?

Ans: A triangle with all three sides of different lengths is called a scalene triangle.

6. What is triangle inequality?

Ans: Triangle inequality states that the sum of the lengths of any two sides of a triangle must be greater than the third side.

7. Can a triangle be formed with sides 3 cm, 4 cm, and 8 cm? Why or why not?

Ans: No, because 3 + 4 = 7 < 8. It does not satisfy triangle inequality.

8. What is the angle sum property of a triangle?

Ans: The sum of the three interior angles of any triangle is always 180°.

9. What is an exterior angle of a triangle?

Ans: It is the angle formed between one side of a triangle and the extension of an adjacent side.

10. What is the relation between an exterior angle and the interior opposite angles?

Ans: The exterior angle is equal to the sum of the two interior opposite angles.

11. What is an altitude of a triangle?

Ans: An altitude is a perpendicular line drawn from a vertex to the opposite side (or its extension).

12. How many altitudes does a triangle have?

Ans: A triangle has three altitudes, one from each vertex.

13. Can a triangle have more than one right angle?

Ans: No, because the sum of angles in a triangle is 180°, and two right angles would already make 180°.

14. What is a right-angled triangle?

Ans: A triangle that has one angle equal to 90° is called a right-angled triangle.

15. How do you check if a triangle can be formed using three lengths without construction?

Ans: By checking if all three sides satisfy the triangle inequality condition.

16. If two angles of a triangle are given, how do you find the third angle?

Ans: Subtract the sum of the given two angles from 180°.

17. What kind of triangle has all angles less than 90°?

Ans: An acute-angled triangle.

18. What kind of triangle has one angle more than 90°?

Ans: An obtuse-angled triangle.

19. When given two angles and an included side, can a triangle always be constructed?

Ans: No, if the sum of the two angles is 180° or more, a triangle is not possible.

20. Why do we use a set square for drawing altitudes in a triangle?

Ans: Because it helps draw an accurate 90° perpendicular line from a vertex to the opposite side.