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

Question. When constructing a triangle with sides 4 cm, 5 cm, and 8 cm, why do the circles intersect?
(a) Sum of smaller sides equals the longest side
(b) Sum of smaller sides is less than the longest side
(c) Sum of smaller sides is greater than the longest side
(d) Sum of smaller sides is zero

Answer: C

Question. A set of lengths is 5, 5, 5. Does an equilateral triangle exist with these side lengths?
(a) No, only if the sides are different
(b) No, because 5+5 is not greater than 5
(c) Yes, because 5+5 > 5
(d) Yes, but only if the angles are not fixed

Answer: C

Question. When constructing a triangle, if two sides and the angle included between them are given, this is what kind of construction case?
(a) ASA
(b) AAS
(c) SAS
(d) SSS

Answer: C

Question. To construct △ABC with AB = 5 cm, AC = 4 cm and ∠ A = 45°, what is the second step after drawing base AB = 5 cm?
(a) Join BC
(b) Mark C such that AC = 4 cm
(c) Draw ∠ A = 45°
(d) Draw a perpendicular line

Answer: C

Question. What happens when the sum of the two smaller side lengths equals the longest side length?
(a) Circles intersect internally
(b) Circles touch each other at a point
(c) Circles do not intersect
(d) A right-angled triangle is formed

Answer: B

Question. If we are given two sides and the included angle (SAS), is it possible for a triangle construction to be impossible?
(a) Yes, if the sides are very large
(b) Yes, if the sides are very small
(c) Only if the included angle is 180° or more
(d) No, a triangle always exists in the SAS case

Answer: C

Question. If the included angle in an SAS construction is 210°, can a triangle be constructed?
(a) Yes
(b) Yes, if the sides are small
(c) No, triangle construction is not possible
(d) Only in an obtuse triangle

Answer: C

Question. When constructing a triangle with Two Angles and the Included Side (ASA), the given side must be called the what?
(a) Opposite side
(b) Longest side
(c) Included side
(d) Hypotenuse

Answer: C

Question. Which set of side lengths results in circles that do not intersect during construction?
(a) 4 cm, 5 cm, 8 cm
(b) 2 cm, 3 cm, 6 cm
(c) 3 cm, 4 cm, 7 cm
(d) 5 cm, 5 cm, 8 cm

Answer: B

Question. To construct △ABC where AB = 5 cm, ∠ A = 45° and ∠ B = 80°, after drawing base AB, we draw the two angles. The point where the two non-base arms meet is what?
(a) Point X
(b) Midpoint M
(c) Third vertex C
(d) Vertex A

Answer: C

Question. For a triangle to exist when two angles are given (like ∠ A and ∠ B), the sum of these two angles must be how much compared to 180°?
(a) Equal to 180°
(b) Greater than 180°
(c) Less than 180°
(d) Equal to 90°

Answer: C

Question. If two given angles are 120° and 100°, can a triangle be formed?
(a) Yes, because they are obtuse
(b) Yes, if the side is short
(c) No, because their sum is greater than 180°
(d) Yes, if they are the two acute angles

Answer: C

Question. If two base angles of a potential triangle are 90° and 90°, what happens to the sides drawn from the base?
(a) They meet at 0°
(b) They form a right angle
(c) They do not meet (they are parallel)
(d) They form an acute triangle

Answer: C

Question. What is the sum of the angles in any triangle?
(a) 90°
(b) 180°
(c) 270°
(d) 360°

Answer: B

Question. If one base angle ∠ A is 40°, for the lines NOT to meet and form a triangle, the other angle ∠ B must be equal to or greater than what value?
(a) 40°
(b) 90°
(c) 140°
(d) 180°

Answer: C

Question. The smallest angle ∠ B for which the two lines will not meet when ∠ A = 40° is formed by a line parallel to the line from A. This smallest non-meeting angle ∠ B is found using which angle property?
(a) Corresponding angles
(b) Vertically opposite angles
(c) Internal angles on the same side of the transversal adding up to 180°
(d) Alternate angles

Answer: C

Question. When two angles are given, does the length of the included side AB affect the possibility of the triangle existing (meeting or not meeting)?
(a) Yes, longer length makes meeting easier
(b) Yes, shorter length makes meeting easier
(c) No, the length AB does not play any part
(d) It depends on the size of the protractor

Answer: C

Question. If two angles of a triangle are 50° and 60°, what is the third angle?
(a) 60°
(b) 70°
(c) 80°
(d) 90°

Answer: B

Question. For ∠ A = 70°, which supplementary angle ∠ B will make triangle construction impossible?
(a) 100°
(b) 90°
(c) 110° or more
(d) 70°

Answer: C

Question. Given angles 35° and 150°, can they be angles of a triangle?
(a) Yes, because 35° < 180°
(b) Yes, because 150° is obtuse
(c) No, because 35° + 150° is greater than 180°
(d) Yes, if the third angle is small

Answer: C