Regular revision with Class 7 Maths MCQ with Answers and Ganita Prakash Class 7 Maths Chapter 7 A Tale of Three Intersecting Lines MCQ improves accuracy in objective exams.
MCQ on A Tale of Three Intersecting Lines Class 7
A Tale of Three Intersecting Lines MCQ Class 7
Class 7 Maths A Tale of Three Intersecting Lines MCQ
Question 1.
A triangle with two sides equal is called:
(a) Scalene triangle
(b) Equilateral triangle
(c) Isosceles triangle
(d) None of these
Solution:
(c) Isosceles triangle
We know that an isosceles triangle has exactly two equal sides and two equal angles opposite to equal sides.
Thus, a triangle with two equal sides is called isosceles triangle.
Question 2.
An equilateral triangle has angles measuring:
(a) 60°, 60°, 60°
(b) 90°, 45°, 45°
(c) 100°, 40°, 40°
(d) 120°, 30°, 30°
Solution:
(a) 60°, 60°, 60°
We know that all angles are equal in an equilateral triangle and each angle is 60°.
Question 3.
The symbol used to represent a triangle is:
(a) ∆
(b) ∠
(c) ||
(d) ⊥
Solution:
(a) ∆
The triangle is commonly denoted using the symbol ∆ as in ∆ABC. The other symbols given in the options represent angle (∠), two parallel lines (||) and two perpendicular lines (⊥).
Question 4.
Consider AB < BC < CA. Which of the following is sufficient to say ∆ABC exists?
(a) BC + CA > AB
(b) AB + CA > BC
(c) AB + BC > CA
(d) None of these
Solution:
(c) AB + BC > CA
Given, AB < BC < CA If sum of two smaller sides is greater than the third side (longest), then triangle inequality is automatically satisfied four all other combination of sides. Thus AB + BC > CA is sufficient to say ∆ABC exists.
Question 5.
A triangle with sides XY = 6.6 cm, YZ = 6 cm and XZ = 6.6 cm, is:
(a) Isosceles
(b) Scalene
(c) Equilateral
(d) None of these
Solution:
(a) Isosceles
Given, XY = 6.6 cm, YZ = 6 cm and XZ = 6.6 cm
Here, two sides have equal length.
We know that if any two sides of a triangle are equal in length, then it is called an isosceles triangle.
Thus, triangle XYZ is an isosceles triangle.
Question 6.
In a ∆ABC,which of the given condition holds?
(a) AB – BC > CA
(b) AB + BC < CA
(c) AB – BC < CA
(d) AB + CA < BC
Solution:
(c) AB – BC < CA
We know that the sum of any two sides of a triangle is greater than the third sides and the difference between the lengths of any two sides of a triangle is always smaller than the length of the third side. Therefore, AB – BC < CA.
Question 7.
Which of the following is true for an obtuse angled triangle?
(a) One angle = 90°
(b) All angles > 90°
(c) 90° < One angle < 180°
(d) Two angles > 90°
Solution:
(c) 90° < One angle < 180°
We know that if an angle of a triangle is greater than 90° (between 90° and 180°), then it is called an obtuse angled triangle.
Question 8.
If AB = 7 cm, ∠T = 50° and ∠B = 60°, then ∠C =
(a) 60°
(b) 70°
(c) 80°
(d) 100°
Solution:
(b) 70°
Given, AB = 7 cm, ∠A = 50° and ∠B = 60°
We know that the sum of all angles of a triangle is 180°.
∴ ∠A + ∠B + ∠C = 180°
⇒ 50° + 60° + ∠C = 180°
⇒ 110° + ∠C = 180°
⇒ ∠C = 180°- 110° = 70°
Question 9.
If AB = 5 cm, AC = 6 cm and ∠A = 90°, what type of triangle will be constructed?
(a) Acute angled triangle
(b) Right-angled triangle
(c) Obtuse angled triangle
(d) Equilateral triangle
Solution:
(b) Right-angled triangle
Given, AB = 5 cm, AC = 6 cm and ∠A = 90°
As ∠A = 90°, the triangle is a right-angled triangle.
Question 10.
How many altitudes (maximum) can a triangle have?
(a) 1
(b) 2
(c) 3
(d) Depend on type of triangle
Solution:
(c) 3
We know that every triangle has three altitudes, each drawn from a vertex to its opposite side.
Question 11.
Which of the following sets of data is sufficient to construct a triangle?
(i) Two sides and the included angle
(ii) Three angles
(iii) Two angles and the included side
(iv) Three sides
Choose the correct option from the following:
(a) Only (i) and (Hi)
(b) Only (i) and (iv)
(c) Only (i), (ii) and (iii)
(d) (i), (ii), (iii) and (iv)
Solution:
(d) (i), (ii), (iii) and (iv)
Triangles can be constructed if we are given three sides, three angles, two sides with the included angle, or two angles with the included side.
Therefore, all the data sets are sufficient.
Question 12.
Which of the following statements about altitudes of a triangle are correct?
(i) An altitude alwavs lies inside the triangle.
(ii) An altitude can lie outside the triangle.
(iii) Every triangle has three altitudes.
(iv) All three altitudes are equal in length.
Choose the correct option from the following:
(a) Only (i) and (ii)
(b) Only (i) and (iii)
(c) Only (ii) and (iii)
(d) (i), (ii), (iii) and (iv)
Solution:
(c) Only (ii) and (iii)
We know that every triangle has three altitudes, each drawn from a vertex to its opposite side (or its extension).
In right-angled triangles, two altitudes lie along sides of the triangle.
In obtuse-angled triangles, 2 altitudes lie outside the triangle.
In a scalene triangle, all three altitudes are of different lengths.
Thus, statements (ii) and (iii) are true.
A Tale of Three Intersecting Lines Class 7 Assertion and Reason Questions
The following questions are Assertion and Reason based questions. Two statements are given, one labelled as Assertion (A) and the other is labelled as Reason (R). Select the correct answer to these questions from the codes (a), (b), (c) and (d) as given below.
(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.
Question 1.
(A): In ∆ABC, if ∠A = 60° and ∠B = 80°, then ∠C = 40°.
(R): In a triangle, the sum of all the angles is 180°.
Solution:
(a) Both A and R are true and R is the correct explanation of A.
Given, in ∆ABC, ∠d = 60° and ∠B = 80°
We know that the sum of all the angles of a triangle is 180°.
∴ ∠A + ∠B + ∠C = 180°
⇒ 60° + 80° + ∠C = 180°
⇒ 140° + ∠C = 180°
⇒ ∠C = 180°- 140° = 40°
Thus, both Assertion (A) and Reason (R) are true, and Reason (R) is the correct explanation of Assertion (A).
Question 2.
(A): If two angles in a triangle are equal, the third angle must be 90°.
(R): In an isosceles triangle, the two angles are equal
Solution:
(d) A is false but R is true.
We know that if two angles of a triangle areequal, then the triangle is called an isosceles triangle.
Let ∠d and ∠B be the equal angles in ∆ABC. We know that the sum of all angles of a triangle is 180°.
∴ ∠A + ∠B + ∠C = 180°
⇒ ∠A + ∠A + ∠C = 180° [∵ ∠d = ∠B]
⇒ 2∠A + ∠C = 180°
⇒ ∠C = 180° – 2∠d
As we can see that the value of ∠C will be 90° only when ∠d is 45°.
Thus, Assertion (A) is false, but Reason (R) is true.
Question 3.
(A): If one of the interior angles of a triangle is 90°, the adjacent exterior angle is also 90°.
(R): A straight angle measures 180°.
Solution:
(a) Both A and R are true and R is the correct explanation of A.
Given, one of the interior angles of a triangle is 90°.
We know that an interior angle and its adjacent exterior angle form a straight angle.
∴ Interior angle + Adjacent exterior angle = 180°
⇒ 90° + Adjacent exterior angle = 180°
⇒ Adjacent exterior angle = 180° – 90° = 90°
Thus, both Assertion (A) and Reason (R) are true, and Reason (R) is the correct explanation of Assertion (A).
Question 4.
(A): All angles of an acute-angled triangle are less than 90°.
(R): The sum of all angles of a triangle is 180°. equal.
Solution:
(b) Both A and R are true but R is not the correct explanation of A.
We know that if all three angles of a triangle are acute angles (between 0° and 90°), then it is called an acute angled triangle and the sum of all angles of a triangle is 180°.
Thus, both Assertion (A) and Reason (R) are true, but. Reason (R) is not the correct explanation of Assertion (A).
A Tale of Three Intersecting Lines Class 7 Fill in the Blanks
Question 1.
A triangle is a closed figure made up of three ________ line segments.
Solution: non-parallel
We know that a triangle is a closed figure made up of three non-parallel line segments.
Question 2.
Each angle in an equilateral triangle measures _________ degrees.
Solution: 60
We know that each angle in an equilateral triangle measures 60 degrees.
Question 3.
A triangle having all three sides of different lengths is called a _______ triangle.
Solution: scalene
We know that a triangle with all three sides of different lengths is called a scalene triangle.
Question 4.
An altitude of a triangle is a _________ from vertex to the opposite side.
Solution: perpendicular line segment
We know that in a triangle, an altitude is a line drawn from a corner (vertex) straight down to the opposite side, making a right angle (90°) with that side.
Thus, an altitude of a triangle is a perpendicular line segment from vertex to the opposite side.
Question 5.
The sum of the three angles in a triangle is __________ .
Solution: 180°
The sum of the three angles in a triangle is 180°.
Question 6.
In ∆ABC, if ∠A = 45° and ∠B = 65°, then the exterior angle at vertex C is _______ .
Solution: 110°
Given, ∠d = 45° and ∠B = 65°
We know that if a side of a triangle is produced or extended, then the exterior angle formed is equal to the sum of two interior opposite angles. ,
∴ Exterior angle at vertex C = Sum of interior angle at A and interior angle at B
= ∠A + ∠B = 45° + 65° = 110°
Thus, in triangle ABC, if ∠A = 45° and ∠B = 65°, then the exterior angle at vertex C is 110°.