Class 10 Maths Chapter 6: Triangles – Ultimate CBSE Board Exam Mastery Quiz 2024-25

Q1. All circles are __________ and all squares are __________.

Q2. In $\triangle ABC$, $DE \parallel BC$. If $AD = 2.4 \text{ cm}$, $DB = 3.6 \text{ cm}$, and $AC = 5 \text{ cm}$, find $AE$.

Q3. If the corresponding angles of two triangles are equal, then the triangles are similar by which criterion?

Q4. In $\triangle ABC$ and $\triangle DEF$, $\angle A = 47^{\circ}$, $\angle E = 83^{\circ}$, and $\angle C = 50^{\circ}$. Is $\triangle ABC \sim \triangle DEF$?

Q5. In $\triangle ABC$, $D$ and $E$ are points on $AB$ and $AC$ such that $DE \parallel BC$. If $AD = x$, $DB = x - 2$, $AE = x + 2$, and $EC = x - 1$, find the value of $x$.

Q6. A vertical pole of length $6 \text{ m}$ casts a shadow $4 \text{ m}$ long on the ground and at the same time a tower casts a shadow $28 \text{ m}$ long. Find the height of the tower.

Q7. If $\triangle ABC \sim \triangle QRP$, $\frac{ar(\triangle ABC)}{ar(\triangle QRP)} = \frac{9}{4}$, $AB = 18 \text{ cm}$, and $BC = 15 \text{ cm}$, then $PR$ is equal to:

Q8. $D$ and $E$ are respectively the points on the sides $AB$ and $AC$ of a $\triangle ABC$ such that $AD = 2 \text{ cm}$, $BD = 3 \text{ cm}$, $BC = 7.5 \text{ cm}$ and $DE \parallel BC$. Then, length of $DE$ is:

Q9. In the given figure, if $\angle ADE = \angle B$, $AD = 3.8 \text{ cm}$, $AE = 3.6 \text{ cm}$, $BE = 2.1 \text{ cm}$, and $BC = 4.2 \text{ cm}$, find $DE$.

Q10. The areas of two similar triangles are $81 \text{ cm}^2$ and $49 \text{ cm}^2$ respectively. If the altitude of the bigger triangle is $4.5 \text{ cm}$, find the corresponding altitude of the smaller triangle.

Q11. Diagonals of a trapezium $ABCD$ with $AB \parallel DC$ intersect each other at the point $O$. If $AB = 2CD$, find the ratio of the areas of triangles $AOB$ and $COD$.

Q12. If $\triangle ABC \sim \triangle DEF$ and $EF = \frac{1}{3}BC$, then $ar(\triangle DEF) : ar(\triangle ABC)$ is:

Q13. In $\triangle ABC$, $DE \parallel BC$. If $AD/DB = 3/5$ and $AC = 5.6 \text{ cm}$, find $AE$.

Q14. Two triangles are similar if their corresponding sides are __________.

Q15. In $\triangle ABC$, $AB = 6\sqrt{3} \text{ cm}$, $AC = 12 \text{ cm}$ and $BC = 6 \text{ cm}$. The angle $B$ is: