CBSE Class 7 Mathematics A Tale of Three Intersecting Lines MCQs Set 08

Question. Which set of side lengths cannot form a triangle?
(a) 3 cm, 4 cm, 5 cm
(b) 3 cm, 4 cm, 8 cm
(c) 4 cm, 4 cm, 6 cm
(d) 3.5 cm, 3.5 cm, 3.5 cm

Answer: B

Question. If we are constructing an equilateral triangle of side 4 cm, after drawing the base AB = 4 cm, the radii for the arcs from A and B must be how much?
(a) 2 cm
(b) 8 cm
(c) 4 cm
(d) 6 cm

Answer: C

Question. In a triangle construction with sides 4 cm, 5 cm, 6 cm, if AB = 4 cm is the base, the arc from A has radius 5 cm, and the arc from B has radius 6 cm. The intersection of these arcs gives which point?
(a) Vertex A
(b) Midpoint of AB
(c) Vertex C
(d) Center point

Answer: C

Question. When the side lengths are 3 cm, 4 cm, and 8 cm, construction of a triangle is impossible because the longest side (8 cm) is what compared to the sum of the other two sides (3+4)?
(a) Smaller than the sum
(b) Equal to the sum
(c) Greater than the sum
(d) Half the sum

Answer: C

Question. The idea that a direct straight-line path is always the shortest path is used to explain which geometric property of triangles?
(a) Angle Sum Property
(b) Shortest Distance Rule
(c) Triangle Inequality
(d) Parallel Lines Rule

Answer: C

Question. What is the triangle inequality rule for side lengths a, b, and c?
(a) a + b < c
(b) a + b > c
(c) a + b = c
(d) a + b = c

Answer: B

Question. For a triangle with side lengths 10 cm, 15 cm, and 30 cm, if we check the path between C and A (30 cm), the roundabout path via B (10 cm + 15 cm = 25 cm) is what compared to the direct path (30 cm)?
(a) Longer
(b) Equal length
(c) Shorter
(d) Cannot be compared

Answer: C

Question. Since the direct path length CA (30 cm) is longer than the roundabout path CB + BA (25 cm) for the lengths 10, 15, 30, what can we conclude about the triangle?
(a) The triangle must be equilateral
(b) The triangle must be isosceles
(c) The triangle cannot exist
(d) The triangle must be obtuse

Answer: C

Question. What is the name of the rule that says for a triangle to exist, each side length must be smaller than the sum of the other two lengths?
(a) Side Length Property
(b) Construction Law
(c) Triangle Inequality
(d) Longest Side Rule

Answer: C

Question. For a triangle with sides 4 cm, 5 cm, and 8 cm, we only need to check if 8 < 4 + 5 = 9. Why is checking only the longest length sufficient?
(a) Because 4 and 5 are obviously smaller than 8 + 5 and 8 + 4
(b) Because the two smaller sides are always shorter than the largest side
(c) Because if the longest side is smaller than the sum of the other two, the other two comparisons will automatically hold true
(d) Because we only need one check for the triangle inequality

Answer: C

Question. For side lengths 10 cm, 15 cm, and 30 cm, why can't a triangle be formed?
(a) 10 + 15 > 30
(b) 10 + 15 < 30
(c) 10 + 15 = 30
(d) 10 + 30 > 15

Answer: B

Question. If a set of three lengths satisfies the triangle inequality, then what can we say about the construction of a triangle with those lengths?
(a) It is impossible to construct
(b) It might be possible
(c) A triangle exists and can be constructed
(d) It only exists if the angles are 60°

Answer: C

Question. For lengths 4 cm, 5 cm, and 8 cm, if we draw two circles with centers at the ends of the 8 cm base (A and B) and radii 4 cm and 5 cm, the circles will do what?
(a) Touch each other at one point
(b) Not intersect at all
(c) Intersect each other at two points internally
(d) Overlap entirely

Answer: C

Question. For a triangle to be formed, the intersection of the two arcs/circles (with radii equal to the two smaller lengths) must result in which case when the base is the longest side?
(a) Case 1: Circles touch each other
(b) Case 2: Circles do not intersect internally
(c) Case 3: Circles intersect each other internally
(d) The radii are equal to the base length

Answer: C

Question. If the sum of the two smaller lengths is equal to the longest length (e.g., 3, 6, 9), how will the two circles look like during the construction process?
(a) They will intersect at two points
(b) They will not intersect
(c) They will touch each other at one point
(d) They will have different radii

Answer: C

Question. Which set of side lengths satisfies the triangle inequality?
(a) 2 cm, 3 cm, 6 cm
(b) 3 cm, 4 cm, 8 cm
(c) 4 cm, 5 cm, 8 cm
(d) 10 cm, 15 cm, 30 cm

Answer: C

Question. If the sum of the two smaller lengths is less than the longest length (e.g., 2, 2, 5), how will the two circles look like during the construction process?
(a) They will touch
(b) They will intersect
(c) They will not intersect internally
(d) They will form a right angle

Answer: C

Question. Which set of lengths satisfies the triangle inequality and therefore permits triangle existence?
(a) 10, 10, 25
(b) 5, 10, 20
(c) 5, 5, 8
(d) 12, 20, 40

Answer: C

Question. Which statement gives the complete procedure to check the existence of a triangle given three lengths?
(a) Check if the shortest side is less than the longest side
(b) Check if the sum of all sides is 180°
(c) Check if the given set of three lengths satisfies the triangle inequality
(d) Check if the longest length is more than the smallest length

Answer: C

Question. For two given lengths, say 1 cm and 100 cm, the third side length must be strictly between which two values for a triangle to exist?
(a) 1 and 100
(b) 100 and 101
(c) 99 and 101
(d) 0 and 100

Answer: C