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: Option 3

Question 2

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

0) 1.5 cm1) 2.0 cm2) 2.5 cm3) 3.0 cm

Answer

✓ Correct Answer: Option 1

Question 3

Question 4

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

0) 7 cm1) 10 cm2) 13 cm3) 17 cm

Answer

✓ Correct Answer: Option 2

Question 5

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

0) 12 cm1) 18 cm2) 24 cm3) 27 cm

Answer

✓ Correct Answer: Option 1

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: Option 1

Question 7

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

0) \angle P1) \angle Q2) \angle R3) None of the above

Answer

✓ Correct Answer: Option 1

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: Option 2

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: Option 0

Question 10

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

0) 10 m1) 12 m2) 13 m3) 15 m

Answer

✓ Correct Answer: Option 2

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) 1:21) 2:12) 1:43) 4:1

Answer

✓ Correct Answer: Option 3

Question 12

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

0) $60^\circ$1) $45^\circ$2) $90^\circ$3) $120^\circ$

Answer

✓ Correct Answer: Option 2

Question 13

13. The lengths of the diagonals of a rhombus are 16 cm and 12 cm. Then, the length of the side of the rhombus is:

0) 8 cm1) 10 cm2) 14 cm3) 20 cm

Answer

✓ Correct Answer: Option 1

Question 14

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

0) 11.2 cm1) 12.4 cm2) 9.6 cm3) 14.2 cm

Answer

✓ Correct Answer: Option 0

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) 21) 42) 63) 8

Answer

✓ Correct Answer: Option 1

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: Option 0

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 E1) \angle A = \angle D2) \angle B = \angle D3) \angle A = \angle F

Answer

✓ Correct Answer: Option 2

Question 18

18. A ladder 10 m long reaches a window 8 m above the ground. Find the distance of the foot of the ladder from the base of the wall.

0) 4 m1) 6 m2) 8 m3) 12 m

Answer

✓ Correct Answer: Option 1

Question 19

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

0) 1/91) 1/32) 33) 9

Answer

✓ Correct Answer: Option 3

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: Option 0

Accepted Answer

✓ Correct Answer: Option 2

Grade 10 Maths Quiz - Triangles

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

2. In \triangle ABC, DE \parallel BC. If AD = 1.5 cm, DB = 3 cm, and AE = 1 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 cm and BC = 12 cm, then AC measures:

5. \triangle ABC \sim \triangle DEF. If AB = 4 cm, DE = 6 cm, EF = 9 cm, and FD = 12 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 m and 11 m stand vertically on a plane ground. If the distance between their feet is 12 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, $AB = 6\sqrt{3} cm$, AC = 12 cm and BC = 6 cm. The angle B is:

13. The lengths of the diagonals of a rhombus are 16 cm and 12 cm. Then, the length of the side of the rhombus is:

14. Let \triangle ABC \sim \triangle DEF and their areas be, respectively, $64 cm^2$ and $121 cm^2$. If EF = 15.4 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 m long reaches a window 8 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 $\frac{ar(\triangle PQR)}{ar(\triangle ABC)}$.

20. Which of the following statements is FALSE?