Grade 10 Maths Quiz - Triangles | Concept of Maths

Question 1

1. Which of the following is NOT a criterion for similarity of triangles?

0) AA (Angle-Angle)

1) SAS (Side-Angle-Side)

2) SSS (Side-Side-Side)

3) SSA (Side-Side-Angle)

Answer

Correct Answer:

Question 2

2. In \( \triangle ABC \), \( DE \parallel BC \). If \( AD = 1.5 \text{ cm} \), \( DB = 3 \text{ cm} \), and \( AE = 1 \text{ cm} \), then \( EC \) is equal to:

0) \( 1.5 \text{ cm} \)

1) \( 2.0 \text{ cm} \)

2) \( 2.5 \text{ cm} \)

3) \( 3.0 \text{ cm} \)

Answer

Correct Answer:

Question 3

3. The ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides. If the corresponding sides are in the ratio \( 4:9 \), the ratio of their areas is:

0) \( 4:9 \)

1) \( 8:18 \)

2) \( 16:81 \)

3) \( 81:16 \)

Answer

Correct Answer:

Question 4

4. In a right-angled \( \triangle ABC \), right-angled at B, if \( AB = 5 \text{ cm} \) and \( BC = 12 \text{ cm} \), then \( AC \) measures:

0) \( 7 \text{ cm} \)

1) \( 10 \text{ cm} \)

2) \( 13 \text{ cm} \)

Question 5

5. \( \triangle ABC \sim \triangle DEF \). If \( AB = 4 \text{ cm} \), \( DE = 6 \text{ cm} \), \( EF = 9 \text{ cm} \), and \( FD = 12 \text{ cm} \), find the perimeter of \( \triangle ABC \).

0) \( 12 \text{ cm} \)

1) \( 18 \text{ cm} \)

2) \( 24 \text{ cm} \)

3) \( 27 \text{ cm} \)

Answer

Correct Answer:

Question 6

6. If \( \triangle ABC \) is an isosceles right triangle right-angled at C, then \( AB^2 \) is equal to:

0) \( AC^2 \)

1) \( 2AC^2 \)

2) \( 3AC^2 \)

3) \( 4AC^2 \)

Answer

Correct Answer:

Question 7

7. If in \( \triangle PQR \), \( PQ^2 + QR^2 = PR^2 \), then which angle is \( 90^\circ \)?

0) \( \angle P \)

1) \( \angle Q \)

2) \( \angle R \)

3) None of the above

Answer

Correct Answer:

Question 8

8. \( \triangle ABC \sim \triangle PQR \). If \( \angle A = 30^\circ \) and \( \angle R = 70^\circ \), then \( \angle B \) is:

0) \( 30^\circ \)

1) \( 70^\circ \)

2) \( 80^\circ \)

3) \( 100^\circ \)

Answer

Correct Answer:

Question 9

9. In an equilateral triangle of side \( 2a \), what is the length of its altitude?

0) \( a\sqrt{3} \)

1) \( 2a\sqrt{3} \)

2) \( \frac{a\sqrt{3}}{2} \)

3) \( a\sqrt{2} \)

Answer

Correct Answer:

Question 10

10. Two poles of height \( 6 \text{ m} \) and \( 11 \text{ m} \) stand vertically on a plane ground. If the distance between their feet is \( 12 \text{ m} \), what is the distance between their tops?

0) \( 10 \text{ m} \)

1) \( 12 \text{ m} \)

2) \( 13 \text{ m} \)

3) \( 15 \text{ m} \)

Answer

Correct Answer:

Question 11

11. The diagonals of a trapezium \( ABCD \) with \( AB \parallel DC \) intersect at \( O \). If \( AB = 2CD \), find the ratio of the areas of \( \triangle AOB \) and \( \triangle COD \).

0) \( 1:2 \)

1) \( 2:1 \)

2) \( 1:4 \)

3) \( 4:1 \)

Answer

Correct Answer:

Question 12

12. In \( \triangle ABC \), \( AB = 6\sqrt{3} \text{ cm} \), \( AC = 12 \text{ cm} \) and \( BC = 6 \text{ cm} \). The angle B is:

0) \( 60^\circ \)

1) \( 45^\circ \)

2) \( 90^\circ \)

3) \( 120^\circ \)

Answer

Correct Answer:

Question 13

13. The lengths of the diagonals of a rhombus are \( 16 \text{ cm} \) and \( 12 \text{ cm} \). Then, the length of the side of the rhombus is:

0) \( 8 \text{ cm} \)

1) \( 10 \text{ cm} \)

2) \( 14 \text{ cm} \)

3) \( 20 \text{ cm} \)

Answer

Correct Answer:

Question 14

14. Let \( \triangle ABC \sim \triangle DEF \) and their areas be, respectively, \( 64 \text{ cm}^2 \) and \( 121 \text{ cm}^2 \). If \( EF = 15.4 \text{ cm} \), find \( BC \).

0) \( 11.2 \text{ cm} \)

1) \( 12.4 \text{ cm} \)

2) \( 9.6 \text{ cm} \)

3) \( 14.2 \text{ cm} \)

Answer

Correct Answer:

Question 15

15. \( D \) and \( E \) are points on the sides \( AB \) and \( AC \) respectively of a \( \triangle ABC \) such that \( DE \parallel BC \). Find the value of \( x \), when \( AD = x \), \( DB = x - 2 \), \( AE = x + 2 \) and \( EC = x - 1 \).

0) \( 2 \)

1) \( 4 \)

2) \( 6 \)

3) \( 8 \)

Answer

Correct Answer:

Question 16

16. If a line intersects sides \( AB \) and \( AC \) of a \( \triangle ABC \) at \( D \) and \( E \) respectively and is parallel to \( BC \), then \( \frac{AD}{AB} \) equals?

0) \( \frac{AE}{AC} \)

1) \( \frac{AE}{EC} \)

2) \( \frac{EC}{AC} \)

3) \( \frac{DB}{EC} \)

Answer

Correct Answer:

Question 17

17. In \( \triangle ABC \) and \( \triangle DEF \), \( \frac{AB}{DE} = \frac{BC}{FD} \). Then they will be similar if:

0) \( \angle B = \angle E \)

1) \( \angle A = \angle D \)

2) \( \angle B = \angle D \)

3) \( \angle A = \angle F \)

Answer

Correct Answer:

Question 18

18. A ladder \( 10 \text{ m} \) long reaches a window \( 8 \text{ m} \) above the ground. Find the distance of the foot of the ladder from the base of the wall.

0) \( 4 \text{ m} \)

1) \( 6 \text{ m} \)

2) \( 8 \text{ m} \)

3) \( 12 \text{ m} \)

Answer

Correct Answer:

Question 19

19. If \( \triangle ABC \sim \triangle PQR \) with \( \frac{BC}{QR} = \frac{1}{3} \), then find the value of \( \frac{\text{ar}(\triangle PQR)}{\text{ar}(\triangle ABC)} \).

0) \( 1/9 \)

1) \( 1/3 \)

2) \( 3 \)

3) \( 9 \)

Answer

Correct Answer:

Question 20

20. Which of the following statements is FALSE?

0) All isosceles triangles are similar.

1) All equilateral triangles are similar.

2) All circles are similar.

3) All squares are similar.

Answer

Correct Answer:

Accepted Answer

Correct Answer:

Grade 10 Maths: Master the Concepts of Triangles | Concept of Maths

Grade 10 Maths: Master the Concepts of Triangles | Concept of Maths

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5. \( \triangle ABC \sim \triangle DEF \). If \( AB = 4 \text{ cm} \), \( DE = 6 \text{ cm} \), \( EF = 9 \text{ cm} \), and \( FD = 12 \text{ cm} \), find the perimeter of \( \triangle ABC \).

6. If \( \triangle ABC \) is an isosceles right triangle right-angled at C, then \( AB^2 \) is equal to:

7. If in \( \triangle PQR \), \( PQ^2 + QR^2 = PR^2 \), then which angle is \( 90^\circ \)?

8. \( \triangle ABC \sim \triangle PQR \). If \( \angle A = 30^\circ \) and \( \angle R = 70^\circ \), then \( \angle B \) is:

9. In an equilateral triangle of side \( 2a \), what is the length of its altitude?

10. Two poles of height \( 6 \text{ m} \) and \( 11 \text{ m} \) stand vertically on a plane ground. If the distance between their feet is \( 12 \text{ m} \), what is the distance between their tops?

11. The diagonals of a trapezium \( ABCD \) with \( AB \parallel DC \) intersect at \( O \). If \( AB = 2CD \), find the ratio of the areas of \( \triangle AOB \) and \( \triangle COD \).

12. In \( \triangle ABC \), \( AB = 6\sqrt{3} \text{ cm} \), \( AC = 12 \text{ cm} \) and \( BC = 6 \text{ cm} \). The angle B is:

13. The lengths of the diagonals of a rhombus are \( 16 \text{ cm} \) and \( 12 \text{ cm} \). Then, the length of the side of the rhombus is:

14. Let \( \triangle ABC \sim \triangle DEF \) and their areas be, respectively, \( 64 \text{ cm}^2 \) and \( 121 \text{ cm}^2 \). If \( EF = 15.4 \text{ cm} \), find \( BC \).

15. \( D \) and \( E \) are points on the sides \( AB \) and \( AC \) respectively of a \( \triangle ABC \) such that \( DE \parallel BC \). Find the value of \( x \), when \( AD = x \), \( DB = x - 2 \), \( AE = x + 2 \) and \( EC = x - 1 \).

16. If a line intersects sides \( AB \) and \( AC \) of a \( \triangle ABC \) at \( D \) and \( E \) respectively and is parallel to \( BC \), then \( \frac{AD}{AB} \) equals?

17. In \( \triangle ABC \) and \( \triangle DEF \), \( \frac{AB}{DE} = \frac{BC}{FD} \). Then they will be similar if:

18. A ladder \( 10 \text{ m} \) long reaches a window \( 8 \text{ m} \) above the ground. Find the distance of the foot of the ladder from the base of the wall.

19. If \( \triangle ABC \sim \triangle PQR \) with \( \frac{BC}{QR} = \frac{1}{3} \), then find the value of \( \frac{\text{ar}(\triangle PQR)}{\text{ar}(\triangle ABC)} \).

20. Which of the following statements is FALSE?

Grade 10 Maths Quiz - Triangles | Concept of Maths

1. Which of the following is NOT a criterion for similarity of triangles?

2. In \( \triangle ABC \), \( DE \parallel BC \). If \( AD = 1.5 \text{ cm} \), \( DB = 3 \text{ cm} \), and \( AE = 1 \text{ cm} \), then \( EC \) is equal to:

3. The ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides. If the corresponding sides are in the ratio \( 4:9 \), the ratio of their areas is:

4. In a right-angled \( \triangle ABC \), right-angled at B, if \( AB = 5 \text{ cm} \) and \( BC = 12 \text{ cm} \), then \( AC \) measures:

Grade 10 Maths: Master the Concepts of Triangles | Concept of Maths

Grade 10 Maths: Master the Concepts of Triangles | Concept of Maths

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5. \( \triangle ABC \sim \triangle DEF \). If \( AB = 4 \text{ cm} \), \( DE = 6 \text{ cm} \), \( EF = 9 \text{ cm} \), and \( FD = 12 \text{ cm} \), find the perimeter of \( \triangle ABC \).

6. If \( \triangle ABC \) is an isosceles right triangle right-angled at C, then \( AB^2 \) is equal to:

7. If in \( \triangle PQR \), \( PQ^2 + QR^2 = PR^2 \), then which angle is \( 90^\circ \)?

8. \( \triangle ABC \sim \triangle PQR \). If \( \angle A = 30^\circ \) and \( \angle R = 70^\circ \), then \( \angle B \) is:

9. In an equilateral triangle of side \( 2a \), what is the length of its altitude?

10. Two poles of height \( 6 \text{ m} \) and \( 11 \text{ m} \) stand vertically on a plane ground. If the distance between their feet is \( 12 \text{ m} \), what is the distance between their tops?

11. The diagonals of a trapezium \( ABCD \) with \( AB \parallel DC \) intersect at \( O \). If \( AB = 2CD \), find the ratio of the areas of \( \triangle AOB \) and \( \triangle COD \).

12. In \( \triangle ABC \), \( AB = 6\sqrt{3} \text{ cm} \), \( AC = 12 \text{ cm} \) and \( BC = 6 \text{ cm} \). The angle B is:

13. The lengths of the diagonals of a rhombus are \( 16 \text{ cm} \) and \( 12 \text{ cm} \). Then, the length of the side of the rhombus is:

14. Let \( \triangle ABC \sim \triangle DEF \) and their areas be, respectively, \( 64 \text{ cm}^2 \) and \( 121 \text{ cm}^2 \). If \( EF = 15.4 \text{ cm} \), find \( BC \).

15. \( D \) and \( E \) are points on the sides \( AB \) and \( AC \) respectively of a \( \triangle ABC \) such that \( DE \parallel BC \). Find the value of \( x \), when \( AD = x \), \( DB = x - 2 \), \( AE = x + 2 \) and \( EC = x - 1 \).

16. If a line intersects sides \( AB \) and \( AC \) of a \( \triangle ABC \) at \( D \) and \( E \) respectively and is parallel to \( BC \), then \( \frac{AD}{AB} \) equals?

17. In \( \triangle ABC \) and \( \triangle DEF \), \( \frac{AB}{DE} = \frac{BC}{FD} \). Then they will be similar if:

18. A ladder \( 10 \text{ m} \) long reaches a window \( 8 \text{ m} \) above the ground. Find the distance of the foot of the ladder from the base of the wall.

19. If \( \triangle ABC \sim \triangle PQR \) with \( \frac{BC}{QR} = \frac{1}{3} \), then find the value of \( \frac{\text{ar}(\triangle PQR)}{\text{ar}(\triangle ABC)} \).

20. Which of the following statements is FALSE?