Extra Questions for Class 7 Maths Chapter 7: A Tale of Three Intersecting Lines – HOTS

Fresh HOTS practice questions for Class 7 Maths Chapter 7 “A Tale of Three Intersecting Lines”, testing the triangle inequality, angle sum property, and exterior angle theorem with new numbers. These Class 7 Mathematics Chapter 7 important questions are handy for last-minute exam practice.

Q1.

Can a triangle have side lengths 6 cm, 7 cm, and 14 cm? Justify your answer.

Answer: No. Since 6+7 = 13, which is less than 14, the triangle inequality fails, so this triangle cannot exist.

Q2.

Two sides of a triangle are 9 cm and 4 cm. What is the range of possible values for the third side?

Answer: The third side must satisfy (9−4) < third side < (9+4), i.e., strictly between 5 cm and 13 cm.

Q3. Assertion-Reason

Assertion (A): A triangle with angles 100°, 50°, 40° is valid.
Reason (R): The three angles must sum to 180°.

Answer: R is true, but A is false (100+50+40 = 190° ≠ 180°), so this angle set is invalid. Since A is false, the combined statement is incorrect.

Q4.

In a triangle, one angle is 90° and another is 35°. Find the third angle and classify the triangle by its angles.

Answer: Third angle = 180 − 90 − 35 = 55°. Since one angle is exactly 90°, this is a right-angled triangle.

Q5. Spot the error

A student says: “Since 4+5=9 and the third side is 9, a triangle with sides 4, 5, 9 is valid.” Identify and correct the error.

Answer: This is incorrect. The triangle inequality requires the sum of two sides to be strictly greater than the third side, not equal to it. Since 4+5=9 exactly equals the third side, the triangle is degenerate (the three points would be collinear) and does not form a valid triangle.

Q6.

The exterior angle of a triangle at vertex C is 130°, and one of the remote interior angles (at A) is 55°. Find the interior angle at B.

Answer: By the Exterior Angle Theorem, exterior angle = sum of remote interior angles: 130 = 55 + angle B, so angle B = 75°.

Q7.

Can an isosceles triangle have angles 50°, 50°, and 80°? Verify and classify the triangle.

Answer: Yes. The angles sum to 50+50+80=180° ✓, and two angles are equal (50° each), confirming it is isosceles. Since all angles are less than 90°, it is also an acute-angled triangle.

Q8.

A triangle has sides 8 cm, 8 cm, and 8 cm. Classify this triangle by both its sides and its angles.

Answer: By sides: equilateral (all three sides equal). By angles: each angle = 180÷3 = 60°, so it is also acute-angled (specifically, equiangular).

Q9.

Two angles of a triangle are 48° and 48°. What type of triangle is this (by sides)?

Answer: Since two angles are equal, the sides opposite them are also equal, making this an isosceles triangle. Third angle = 180−48−48 = 84°.

Q10.

Explain why a triangle can never have two obtuse angles.

Answer: If a triangle had two angles each greater than 90°, their sum alone would already exceed 180°, leaving no room for a positive third angle. Since all three angles must sum to exactly 180°, at most one angle can be obtuse (or right).

NCERT Solutions: Class 7 Maths Chapter 7

Revision Notes: Class 7 Maths Chapter 7 Revision Notes

Written by Satish

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