Question

Class 7 Maths MCQ Questions for The Triangles and its Properties with Answers?

Answer 1

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Practice MCQ Questions for Class 7 Maths

1. If all the three sides of a triangle are equal, the triangle is called

(a) equilateral
(b) right-angled
(c) isosceles
(d) scalene.

2. If all the angles of a triangle are acute, the triangle is called

(a) obtuse-angled
(b) acute-angled
(c) right-angled
(d) none of these

3. If one angle of a triangle measures 90°, the triangle is called

(a) acute-angled
(b) obtuse-angled
(c) right-angled
(d) none of these

4. How many medians can a triangle have?

(a) 1
(b) 2
(c) 3
(d) 4

5. If p: The total measure of the three angles of a triangle is 180º and q: Sum of the length of any two sides of a triangle is less than the length of the third side, then which of the following options hold?

(a) Both p and q are true
(b) p is true and q is false
(c) p is false and q is true
(d) Both p and q are false

6. The measure of each angle of an equilateral triangle is

(a) 30º
(b) 45º
(c) 90º
(d) 60º

7. Two angles of a triangle measure 90º and 30º. The measure of the third angle is

(a) 90º
(b) 30º
(c) 60º
(d) 120º

8. The ratio of the measures of the three angles of a triangle is 2 : 3 : 4. The measure of the largest angle is

(a) 80º
(b) 60º
(c) 40º
(d) 180º

9. In the following figure, m || QR. Then, the measure of ∠QPR is

(a) 80º
(b) 85º
(c) 75º
(d) 70º

10. In the following figure, ∆ ABC is an equilateral triangle. Find ∠x.

(a) 30º
(b) 45º
(c) 60º
(d) 90º

11. In the following figure, find ∠ x and ∠ y, if ∠x – ∠y – 10º

(a) 65º, 55º
(b) 55º, 45º
(c) 45º, 35º
(d) 60º, 60º

12. In the following figure, one angle of triangle ABC is 40º. If the difference of the other two angles is 30°, find the larger of the other two angles.

(a) 85º
(b) 80º
(c) 75º
(d) 70º

13. In which case of the following lengths of sides of a triangle, is it possible to draw a triangle?

(а) 3 cm, 4 cm, 7 cm
(b) 2 cm, 3 cm, 7 cm
(c) 3 cm, 4 cm, 5 cm
(d) 3 cm, 3 cm, 7 cm

14. Which of the following cannot be the sides of a right triangle?

(а) 2 cm, 2 cm, 4 cm
(b) 5 cm, 12 cm, 13 cm
(c) 6 cm, 8 cm, 10 cm
(d) 3 cm, 4 cm, 5 cm

15. Find angle x in the following figure:

(a) 90°
(b) 80°
(c) 95°
(d) 100°

16. Find angle x in the following figure:

(a) 58°
(b) 59°
(c) 57°
(d) 56°

17. A triangle has how many sides :

(a) three
(b) five
(c) four
(d) None of these

18. If two sides of a triangle are added then the result is :

(a) greater than third
(b) less than third
(c) equal to third
(d) none of these

19. Vikash wants to plant a flower on the ground in the form of a rhombus. The diagonals of the rhombus measure 42 cm and 56 cm. Find the perimeter of the field.

(a) 150 cm
(b) 140 cm
(c) 130cm
(d) 120cm

20. Which is the longest side of a right triangle?

(a) Base
(b) Perpendicular
(c) Hypotenuse
(d) None of these

21. If two sides of a triangle are not equal the triangle is called

(a) scalene
(b) isosceles
(c) equilateral
(d) right-angled

22. ABC is an isosceles triangle with AB = AC and AD is altitude, then ____.

(a) ∠B>∠C             
(b) ∠B<∠C 
(c) ∠B=∠C  
(d) None of these

23. In a ΔABC, which of the given condition holds?

(a) AB−BC>CA
(b) AB+BC<CA
(c) AB−BC<CA
(d) AB+CA<BC

24. Maximum number of possible obtuse angles in a triangle is:

(a) 0
(b) 1
(c) 2
(d) 3

25. In the following figure, find x if BA || CE.

(a) 60°
(b) 40°
(c) 45°
(d) 65°

Answer 2

1. Answer: (a) equilateral

Explanation: A triangle with all sides equal is called an equilateral triangle, and a triangle with no sides equal is called a scalene triangle. An equilateral triangle is therefore a special case of an isosceles triangle having not just two, but all three sides and angles equal.

2.  Answer: (b) acute-angled

Explanation: An equilateral triangle is a triangle with all three angles and sides equal. If all a triangle's angles are equal, they all must measure 60 degrees, adding up to 180 degrees total. Since all angles are acute, or less than 90 degrees, an equilateral triangle is also an acute triangle.

3.  Answer:(c) right-angled

Explanation: A triangle one of whose angles is 90 degree is called right angled triangle.

4.  Answer: (c) 3

Explanation: A triangle has 3 medians. The perpendicular line segment from a vertex of a triangle to its opposite side is called an altitude of the triangle. A triangle has 3 altitudes.

5.  Answer: (b) p is true and q is false

Explanation: Theorem: In any triangle, the sum of any two sides is greater than the third side. Also, the difference between any two sides must be smaller than the third side.

Theorem: The sum of all three interior angles of a triangle is 180º

Hence, p is true and q is false.

For q to be true, the sum of the length of any two sides of a triangle is 'more' than the length of the third side.

6.  Answer: (d) 60º

Explanation: xº + xº + xº = 180º

 ⇒ xº = 60º.

7.  Answer: (c) 60º

Explanation: Third angle = 180º – (90º + 30º) 

= 60º.

8. Answer: (a) 80º

Explanation: Largest angle = \(\frac{4}{2+3+4}\times180º\)

=  80º

9.  Answer: (b) 85º

Explanation: ∠PQR = 50º

∴ ∠QPR – 180º – (50º + 45º) 

= 85º.

10. Answer: (a) 60º

Explanation: ∠ABC = 60º.

∴ ∠ABD = 180º – 60° = 120º

∴ x = 180º – (120º + 30º) 

= 30º

11.  Answer: (a) 65º, 55º

Explanation: ∠x + ∠y = 120º; ∠x – ∠y = 10º 

∠x = 65º, ∠y = 55º.

12.  Answer: (a) 85º

Explanation: x + y = 180° – 40° = 140° x – y = 30°. 

 x = 85°.

13.  Answer: (c) 3 cm, 4 cm, 5 cm

Explanation: 3 + 4 > 5; 4 + 5 > 3; 5 + 3 > 4.

14.  Answer: (а) 2 cm, 2 cm, 4 cm

Explanation: 2² + 2² = 8;

4² = 16

∴ 2² + 2² ≠ 4²

15. Answer: (a) 90°

Explanation: x + 45 + 45° = 180°

⇒ x = 90°.

16.  Answer: (a) 58°

Explanation: x + x = 116°

⇒ x = 58°.

17.  Answer: (a) three

Explanation: A triangle is a closed figure of three sides.

18.  Answer: (a) greater than third

Explanation: As the sum of the length of any two sides of a triangle is greater than the third side.

19.  Answer: (b) 140 cm

Explanation: Since diagonals of a rhombus bisect each other at 90°

Given, BD=42 cm and AC=56 cm

Since BK = 1/2 BD = 42/2 = 21 cm

Thus AK = 1/2 AC = 56/2 = 28 cm

In △KAB, we have 

AB² = AK² + BK²

= (28)² + (21)²

= 784 + 441 

= 1225

Thus AB = \(\sqrt{1225}\) = 35 cm

Therefore, perimeter of the field ABCD = 4×35 = 140 cm

20.  Answer: (c) Hypotenuse

Explanation: The longest side of the right-angled triangle is called its Hypotenuse.

21.  Answer: (a) scalene

Explanation: An isosceles triangle therefore has both two equal sides and two equal angles. . A triangle with all sides equal is called an equilateral triangle, and a triangle with no sides equal is called a scalene triangle.

22.  Answer: (c) ∠B=∠C  

Explanation: In the given triangle ΔABC:

AB=AC

AD is perpendicular

So in ΔADC,ΔADB

AD = AD Common

ΔADC = ΔADB = 90°

ΔADC ≅ ΔADB

⟹∠B =∠C.

23.  Answer: (c) AB−BC<CA

Explanation: Theorem: In any triangle, sum of any two sides is greater than the third side. Also, the difference of any two sides must be smaller than the third side.Therefore, in an △ABC, AB−BC<CA and AB+BC>CA.

24.  Answer: (b) 1

Explanation: Any triangle must have interior angles that add up to 180°. An obtus angle is an angle greater than 90° but less than 180° If you an angle that was 91°. The other 2 angles would have to be acute . This is because the other angles would take up 180° − 91°  = 89°of the triangle . Since 89° is less than 90°, this means the other 2 angles must both be acute.You are left with 1 obtuse angle.

25.  Answer: (d) 65°

Explanation: ∠ECD = ∠ABC = 50°;

∴ x = 180° – (65°+ 50°) 

= 65°.

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