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07
NCERT Solutions · Maths Ch 7
A Tale of Three Intersecting Lines
15 questions · 2 exercises
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Ex 7.1
Ex 7.2
NCERT answers with full exam-style working, step by step. Tap a question to open its solution.
1
EXERCISE 7.1 · 12 QUESTIONS
Isosceles Triangles and the Triangle Inequality
Q1
Use the points on the circle and/or the centre to form isosceles triangles (Fig. on page 150).
(2 marks)
Q2
Use the points on the circles and/or their centres to form isosceles and equilateral triangles. The circles are of the same size.
(3 marks)
Q3
We checked by construction that there are no triangles having sidelengths 3 cm, 4 cm and 8 cm, and 2 cm, 3 cm and 6 cm. Check if you could have found this without trying to construct the triangle.
(3 marks)
Q4
Can we say anything about the existence of a triangle for each of the following sets of lengths? (a) 10 km, 10 km and 25 km (b) 5 mm, 10 mm and 20 mm (c) 12 cm, 20 cm and 40 cm
(3 marks)
Q5
Will this always happen? That is, for any set of lengths, will there be at least two comparisons where the direct length is less than the sum of the other two? Explore for different sets.
(3 marks)
Q6
Which of the following lengths can be the sidelengths of a triangle? Explain your answers. (a) 2, 2, 5 (b) 3, 4, 6 (c) 2, 4, 8 (d) 5, 5, 8 (e) 10, 20, 25 (f) 10, 20, 35 (g) 24, 26, 28
(3 marks)
Q7
Check if a triangle exists for each set of lengths: (a) 1, 100, 100 (b) 3, 6, 9 (c) 1, 1, 5 (d) 5, 10, 12
(3 marks)
Q8
Does there exist an equilateral triangle with sides 50, 50, 50? In general, does there exist an equilateral triangle of any sidelength? Justify your answer.
(2 marks)
Q9
For each of the following, give at least 5 possible values for the third length so that a triangle exists (decimals can be chosen): (a) 1, 100 (b) 5, 5 (c) 3, 7
(3 marks)
Q10
Is there a combination of measurements, for two sides and the included angle, where a triangle is not possible? Justify your answer using what you observe during construction.
(2 marks)
Q11
For each of the following angles, find another angle for which a triangle is (a) possible, (b) not possible. Find at least two angles for each category: (a) 30° (b) 70° (c) 54° (d) 144°
(3 marks)
Q12
Determine which of the following pairs can be the angles of a triangle and which cannot: (a) 35°, 150° (b) 70°, 30° (c) 90°, 85° (d) 50°, 150°. Can you form a rule for the two angles for which a triangle is possible?
(3 marks)
2
EXERCISE 7.2 · 3 QUESTIONS
Angles of a Triangle
Q13
Find the third angle of a triangle (using a parallel line) when two of the angles are: (a) 36°, 72° (b) 150°, 15° (c) 90°, 30° (d) 75°, 45°
(3 marks)
Q14
Can you construct a triangle all of whose angles are equal to 70°? If two of the angles are 70°, what would the third angle be? If all the angles in a triangle have to be equal, then what must its measure be?
(3 marks)
Q15
In a triangle ABC, ∠B = ∠C and ∠A = 50°. Find ∠B and ∠C.
(3 marks)