Official CBSE Assignments for Class 7 Mathematics
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Solved Practice Assignments for Mathematics
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This is Practice Paper 20 for CBSE Class 7 Maths Ganita Prakash Chapter 7, A Tale of Three Intersecting Lines: a 40-mark paper with 20 questions in Sections A to E, each followed by a worked answer. The questions focus on the triangle inequality and how the construction circles behave, right-angled triangles such as 5, 12, 13, altitudes of acute-angled triangles, finding missing interior and exterior angles, and constructing a triangle from its three sides (5 cm, 6 cm and 7 cm).
Section A: Multiple Choice Questions (1 Mark Each)
(a) A triangle can be formed
(b) A triangle cannot be formed
(c) A right-angled triangle is formed
(d) An equilateral triangle is formed
Show Answer & Explanation
Answer: (b) A triangle cannot be formed
Explanation:
1. Longest stick = 11 cm. Sum of the other two = 4 + 6 = 10 cm.
2. 10 cm is less than 11 cm, so the two short sticks cannot reach each other over the 11 cm stick.
3. The triangle inequality fails, so a triangle cannot be formed.
Teacher's Note:
1. The two shorter sides together must be longer than the longest side.
2. Options (c) and (d) are impossible once (b) is true.
(a) Do not intersect
(b) Touch externally
(c) Intersect at two points
(d) Coincide completely
Show Answer & Explanation
Answer: (c) Intersect at two points
Explanation:
1. Draw the third side as the base and draw circles from its two ends with the other two sides as radii.
2. When the two radii together are longer than the base, the circles overlap and cross each other at two points, one above and one below the base.
3. Either crossing point can be the third vertex. So the circles intersect at two points.
Teacher's Note:
1. Sum greater: two crossing points. Sum equal: the circles touch at one point. Sum smaller: no crossing.
2. The two crossing points give two mirror-image copies of the same triangle.
(a) Right-angled
(b) Obtuse-angled
(c) Acute-angled
(d) Isosceles
Show Answer & Explanation
Answer: (c) Acute-angled
Explanation:
1. The largest angle is 70°, which is less than 90°.
2. So all three angles are acute and the triangle is acute-angled.
3. All angles are different, so it is not isosceles.
Teacher's Note:
1. Check the sum first: 50° + 60° + 70° = 180°.
2. The largest angle decides acute, right or obtuse.
(a) Acute-angled triangle
(b) Obtuse-angled triangle
(c) Equilateral triangle
(d) Right-angled triangle
Show Answer & Explanation
Answer: (d) Right-angled triangle
Explanation:
1. A right-angled triangle is defined as a triangle with one angle of 90°.
2. It cannot have two right angles, because 90° + 90° already uses up all 180°.
3. So the answer is the right-angled triangle.
Teacher's Note:
1. Acute: all angles below 90°. Obtuse: one angle above 90°. Right: one angle exactly 90°.
2. An equilateral triangle has all angles 60°.
(a) Acute-angled scalene
(b) Right-angled scalene
(c) Obtuse-angled isosceles
(d) Equilateral
Show Answer & Explanation
Answer: (b) Right-angled scalene
Explanation:
1. All three sides are different, so the triangle is scalene.
2. Compare the squares: 5² + 12² = 25 + 144 = 169, and 13² = 169.
3. When the squares of the two shorter sides add up exactly to the square of the longest side, the angle between the two shorter sides is 90° (construct it to scale and measure: it is a right angle).
4. Hence the triangle is right-angled scalene.
Teacher's Note:
1. 5, 12, 13 is a famous right-triangle set, like 3, 4, 5.
2. If the sum of squares is more than the square of the longest side the triangle is acute; if less, obtuse.
(a) Outside the triangle
(b) On one side of the triangle
(c) Inside the triangle
(d) Coinciding with the base
Show Answer & Explanation
Answer: (c) Inside the triangle
Explanation:
1. An altitude is the perpendicular from a vertex to the opposite side.
2. In an acute-angled triangle every angle is less than 90°, so the foot of each perpendicular falls between the ends of the opposite side.
3. So every altitude lies inside the triangle.
Teacher's Note:
1. Right-angled: two altitudes are sides. Obtuse-angled: two altitudes fall outside.
2. All three altitudes of an acute-angled triangle meet at a point inside it.
(a) 65°
(b) 70°
(c) 75°
(d) 85°
Show Answer & Explanation
Answer: (c) 75°
Explanation:
1. Exterior angle = sum of the two interior opposite angles.
2. 55° + other angle = 130°.
3. Other angle = 130° − 55° = 75°.
Teacher's Note:
1. Check: the third angle is 180° − 130° = 50°, and 55° + 75° + 50° = 180°.
2. Subtract the known interior angle from the exterior angle.
(a) Scalene
(b) Isosceles
(c) Right-angled
(d) Equilateral
Show Answer & Explanation
Answer: (d) Equilateral
Explanation:
1. Two triangles are similar when they have the same shape (the same angles), even if their sizes differ.
2. Every equilateral triangle has angles 60°, 60° and 60°, so all equilateral triangles have the same shape.
3. Scalene, isosceles and right-angled triangles can have many different sets of angles, so they are not always the same shape.
4. Hence the answer is equilateral.
Teacher's Note:
1. A small and a large equilateral triangle look exactly alike, one is just an enlargement of the other.
2. Two right-angled triangles, such as 90°, 45°, 45° and 90°, 30°, 60°, have different shapes.
Assertion (A): If the sum of two sides of a triangle is equal to the third side, no triangle is formed.
Reason (R): The circles drawn during construction touch at exactly one point.
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is not the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
Show Answer & Explanation
Answer: (a) Both A and R are true, and R is the correct explanation of A.
Explanation:
1. Assertion: if two sides add up exactly to the third, they lie flat along it, so no triangle is formed. A is true.
2. Reason: in the construction, circles drawn from the ends of the third side with these two lengths as radii meet at only one point, and that point lies on the third side itself. R is true.
3. Since the only meeting point is on the base, there is no third vertex above it, which is exactly why no triangle forms. R explains A.
4. Answer: (a).
Teacher's Note:
1. The construction shows the triangle inequality in action.
2. Two crossing points: triangle. One touching point: a flat line. No meeting: nothing.
Assertion (A): The sum of any two interior angles of a triangle is always less than 180°.
Reason (R): The sum of all interior angles of a triangle is 180°.
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is not the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
Show Answer & Explanation
Answer: (a) Both A and R are true, and R is the correct explanation of A.
Explanation:
1. Reason: the angle sum property says the three angles add up to 180°. R is true.
2. Assertion: sum of any two angles = 180° − (third angle). The third angle is always more than 0°, so the sum of the other two is less than 180°. A is true.
3. A follows directly from R, so R is the correct explanation of A. Answer: (a).
Teacher's Note:
1. This is also why a triangle can have at most one right angle or one obtuse angle.
2. Example: 70° + 80° = 150° < 180°, leaving 30° for the third angle.
Section B: Short Answer Questions (2 Marks Each)
Question 11. State the triangle inequality theorem.
Answer:
In any triangle, the sum of the lengths of any two sides is greater than the length of the third side.
For △ABC: AB + BC > AC, BC + CA > AB and CA + AB > BC.
Example: 3 cm, 4 cm, 5 cm can form a triangle because 3 + 4 = 7 > 5.
In simple words: Any two sides of a triangle together are always longer than the third side.
Teacher's Note:
1. Write the statement with the word 'greater', not 'greater than or equal to'.
2. An example makes the statement clear.
Question 12. Find the third angle of a triangle if the other two angles are 45° and 65°.
Answer:
By the angle sum property, the angles add up to 180°.
Sum of the two given angles = 45° + 65° = 110°.
Third angle = 180° − 110° = 70°.
In simple words: Take away the two known angles from 180°.
Teacher's Note:
1. Check: 45° + 65° + 70° = 180°.
2. All angles are below 90°, so this triangle is acute-angled.
Question 13. Name the triangle whose altitude coincides with one of its sides.
Answer:
In a right-angled triangle, the two sides that make the right angle are perpendicular to each other.
So the altitude from one acute-angle vertex to the opposite side is the side itself.
For example, if ∠B = 90° in △ABC, the altitude from A to BC is AB, and the altitude from C to AB is CB.
In simple words: In a right-angled triangle, the two arms of the right angle are already altitudes.
Teacher's Note:
1. Two of the three altitudes coincide with sides; the third (from the right angle) lies inside.
2. Remember: an altitude is a perpendicular from a vertex to the opposite side.
Question 14. Why is an equilateral triangle always acute-angled?
Answer:
In an equilateral triangle all three angles are equal.
By the angle sum property, each angle = 180° ÷ 3 = 60°.
60° is less than 90°, so every angle is acute and the triangle is always acute-angled.
In simple words: Each angle of an equilateral triangle is 60°, which is always less than 90°.
Teacher's Note:
1. The reason must show why each angle is 60°.
2. No equilateral triangle can be right-angled or obtuse-angled.
Section C: Short Answer Questions (3 Marks Each)
Question 15. Check whether a triangle can be formed with sides 7 cm, 10 cm and 12 cm.
Answer:
Longest side = 12 cm.
Sum of the other two sides = 7 + 10 = 17 cm, and 17 cm > 12 cm.
The other pairs are fine too: 7 + 12 = 19 > 10 and 10 + 12 = 22 > 7.
The triangle inequality holds, so a triangle can be formed.
In simple words: The two smaller sides together (17 cm) are longer than the biggest side (12 cm), so a triangle is possible.
Teacher's Note:
1. If the longest side passes the test, the other two checks always pass.
2. All sides are different, so the triangle would be scalene.
Question 16. Find the exterior angle of a triangle if the interior opposite angles are 38° and 52°.
Answer:
Exterior angle = sum of the two interior opposite angles.
Exterior angle = 38° + 52° = 90°.
Check: the interior angle next to it = 180° − 90° = 90°, and 38° + 52° + 90° = 180°. So this triangle is right-angled.
In simple words: Add the two inside angles opposite the exterior angle: 38° + 52° = 90°.
Teacher's Note:
1. An exterior angle of 90° means the adjacent interior angle is also 90°.
2. Always check with the angle sum.
Question 17. Classify a triangle with angles 40°, 50° and 90°.
Answer:
By angles: one angle is exactly 90°, so it is a right-angled triangle.
By sides: all three angles are different, so all three sides are different; it is scalene.
Hence it is a right-angled scalene triangle.
In simple words: It has a 90° corner and no equal angles, so it is right-angled and scalene.
Teacher's Note:
1. Check: 40° + 50° + 90° = 180°.
2. The two acute angles of a right triangle always add up to 90°.
Section D: Long Answer Question (5 Marks)
Question 18. Construct a triangle with sides 5 cm, 6 cm and 7 cm. Explain the steps.
Answer:
First check: 5 + 6 = 11 > 7, so the triangle exists.
Steps of construction:
Step 1: Draw a line segment AB = 5 cm.
Step 2: With A as centre and radius 6 cm, draw an arc above AB.
Step 3: With B as centre and radius 7 cm, draw another arc cutting the first arc at C.
Step 4: Join AC and BC.
△ABC is the required triangle with AB = 5 cm, AC = 6 cm and BC = 7 cm.
In simple words: Draw one side, swing two arcs with the other two lengths from its ends, and join their crossing point.
Teacher's Note:
1. Keep the compass width fixed while drawing each arc.
2. The arcs would also cross below AB; that point gives a mirror image of the same triangle.
3. Do not rub out the arcs; they show your construction.
Section E: Case Study Based Questions (4 Marks Each)
Question 19. Case Study 1: Playground Support Frame
A school plans to install a triangular metal support frame for a swing in the playground. The available metal rods are of lengths 6 m, 8 m and 13 m. Before installation, the sports teacher asks students to verify mathematically whether the rods can form a triangle. This helps ensure safety and prevents wastage of materials by applying geometric principles.
Answer the following questions:
(a) Identify the longest rod.
(b) Find the sum of the other two rods.
(c) Can a triangle be formed?
(d) Name the rule used.
Answer:
(a) The rods are 6 m, 8 m and 13 m, so the longest rod is 13 m.
(b) Sum of the other two rods = 6 m + 8 m = 14 m.
(c) 14 m is greater than 13 m, so yes, a triangle can be formed (only just: the margin is 1 m).
(d) The rule used is the triangle inequality: the sum of any two sides must be greater than the third side.
In simple words: 6 m and 8 m together make 14 m, which beats 13 m, so the rods fit into a triangle.
Teacher's Note:
1. When the margin is small, the triangle will be quite flat, with one large angle.
2. Compare like units: all lengths are in metres.
Question 20. Case Study 2: Decorative Wall Design
An interior designer creates a triangular wall design using two measured angles of 50° and 60°. To complete the design accurately, the third angle must be calculated without measuring it physically. Using a basic triangle property helps achieve symmetry and aesthetic balance in the design.
Answer the following questions:
(a) Name the property used.
(b) Find the third angle.
(c) Classify the triangle by angles.
(d) State whether the triangle is scalene or isosceles.
Answer:
(a) The angle sum property of a triangle (the three angles add up to 180°).
(b) Third angle = 180° − (50° + 60°) = 180° − 110° = 70°.
(c) The angles 50°, 60° and 70° are all less than 90°, so it is an acute-angled triangle.
(d) All three angles are different, so all three sides are different: a scalene triangle.
In simple words: The third angle is 70°; with all angles sharp and different, the triangle is acute-angled and scalene.
Teacher's Note:
1. Equal angles would mean equal sides; here no angles match.
2. Check: 50° + 60° + 70° = 180°.
Free study material for Mathematics
CBSE Class 7 Mathematics Assignments for Chapter 07 A Tale of Three Intersecting Lines
Revision Assignment: Chapter 07 A Tale of Three Intersecting Lines (CBSE)
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