CBSE Class 7 Mathematics A Tale of Three Intersecting Lines MCQs Set 02

Question. If we construct an equilateral triangle of side 4 cm using only a marked ruler, how will it be?
(a) Very easy and fast
(b) Impossible to do
(c) Might require several trials
(d) Only possible if the angle is 60 degrees

Answer: C

Question. Which geometry tool is recalled for efficiently finding a point C that is a specific distance from two points A and B?
(a) Protractor
(b) Ruler only
(c) Compass
(d) Set square

Answer: C

Question. What happens if the sum of two shorter sides equals the third side?
(a) Triangle exists
(b) Triangle is equilateral
(c) Triangle is right-angled
(d) Triangle cannot exist

Answer: D

Question. To construct a triangle when sides are given (like 4 cm, 5 cm, 6 cm), we use the intersection of two things. What are these?
(a) Two lines
(b) One circle and one line
(c) Two arcs (from the circles centered at base vertices)
(d) Two straight edges

Answer: C

Question. In an equilateral triangle construction, if the base AB is 4 cm, the radii of both arcs from A and B must be how much?
(a) 8 cm
(b) 2 cm
(c) 4 cm
(d) 1 cm

Answer: C

Question. A triangle having only two sides of equal length is called what?
(a) Equilateral
(b) Scalene
(c) Isosceles
(d) Right-angled

Answer: C

Question. A triangle where all three sides have different lengths is called what kind of triangle?
(a) Equilateral
(b) Isosceles
(c) Scalene
(d) Acute-angled

Answer: C

Question. In ∆ABC, if ∠A = 50° and ∠B = 60°, what is ∠C?
(a) 70°
(b) 60°
(c) 70°
(d) 80°

Answer: A

Question. For the lengths 3 cm, 4 cm, and 8 cm, is a triangle possible?
(a) Yes, always possible
(b) Yes, if we use a compass
(c) No, triangle construction is impossible
(d) Possible, because 3 + 4 is nearly 8

Answer: C

Question. The direct straight-line path between two points is always what compared to a roundabout path via a third point?
(a) Longer
(b) Equal length
(c) Shorter
(d) Cannot be measured

Answer: C

Question. If we have sidelengths 10 cm, 15 cm, and 30 cm, why can a triangle not exist?
(a) Because 10 + 15 > 30
(b) Because the sides are of different lengths
(c) Because 30 is greater than 10 + 15
(d) Because 10 + 30 is too much

Answer: C

Question. What is the rule where each side length must be smaller than the sum of the other two lengths, tell me?
(a) Angle sum rule
(b) Side length rule
(c) Triangle inequality
(d) Existence rule

Answer: C

Question. Which triangle has all angles equal?
(a) Scalene
(b) Right-angled
(c) Isosceles
(d) Equilateral

Answer: D

Question. Which set of lengths does NOT satisfy the triangle inequality?
(a) 3, 4, 5
(b) 4, 5, 8
(c) 10, 15, 30
(d) 5, 10, 12

Answer: C

Question. Given a set of lengths, how do we efficiently check if a triangle can exist? We check if the longest length is smaller than the sum of the other two lengths. This checks which part of triangle inequality?
(a) Only one comparison is needed
(b) At least two comparisons are needed
(c) Only the longest side check is sufficient
(d) All three comparisons are needed

Answer: C

Question. If the longest side of a potential triangle is 8 cm, and the other two sides are 4 cm and 5 cm, does the triangle inequality hold?
(a) No, because 8 \not< 4+5
(b) Yes, because 8 < 4+5
(c) Yes, because 8 < 9
(d) Yes, because 5 < 8

Answer: C

Question. When constructing a triangle with sides 4, 5, 8, if we take the longest side (8 cm) as the base AB, and draw circles of radii 4 cm (from A) and 5 cm (from B), what happens to the circles?
(a) They touch externally
(b) They do not intersect
(c) They intersect each other internally at two points
(d) They overlap completely

Answer: C

Question. Which condition guarantees triangle existence?
(a) Two sides are equal
(b) All sides are odd numbers
(c) Sides satisfy triangle inequality
(d) Only one large angle

Answer: C

Question. For side lengths 2, 2, 5, can a triangle exist?
(a) Yes, because 2 + 5 > 2
(b) Yes, always
(c) No, because 2 + 2 is less than 5
(d) Cannot tell easily

Answer: C

Question. For side lengths 10, 20, 25, can a triangle exist?
(a) No, because they are too large
(b) No, because 25 > 20 + 10
(c) Yes, because 25 < 10 + 20
(d) Only if we use decimals

Answer: C