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

Question 1

All circles are __________ and all squares are __________.

Accepted Answer

Similar, Similar

Answer

Congruent, Similar

Answer

Similar, Congruent

Answer

Congruent, Congruent

Question 2

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

Accepted Answer

$2 	ext{ cm}$

Answer

$3 	ext{ cm}$

Answer

$1.2 	ext{ cm}$

Answer

$2.4 	ext{ cm}$

Question 3

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

Accepted Answer

AAA

Answer

SSS

Answer

SAS

Answer

RHS

Question 4

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

Accepted Answer

Yes, by AA

Answer

No

Answer

Yes, by SAS

Answer

Data Insufficient

Question 5

In $	riangle 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 $x$.

Accepted Answer

4

Answer

3

Answer

5

Answer

2

Question 6

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

Accepted Answer

$42 	ext{ m}$

Answer

$40 	ext{ m}$

Answer

$38 	ext{ m}$

Answer

$44 	ext{ m}$

Question 7

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

Accepted Answer

$10 	ext{ cm}$

Answer

$12 	ext{ cm}$

Answer

$8 	ext{ cm}$

Answer

$15 	ext{ cm}$

Question 8

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

Accepted Answer

$3 	ext{ cm}$

Answer

$2.5 	ext{ cm}$

Answer

$5 	ext{ cm}$

Answer

$6 	ext{ cm}$

Question 9

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

Accepted Answer

$2.8 	ext{ cm}$

Answer

$2.7 	ext{ cm}$

Answer

$3.2 	ext{ cm}$

Answer

$2.1 	ext{ cm}$

Question 10

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

Accepted Answer

$3.5 	ext{ cm}$

Answer

$2.5 	ext{ cm}$

Answer

$4 	ext{ cm}$

Answer

$3 	ext{ cm}$

Question 11

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 $COD$.

Accepted Answer

$4:1$

Answer

$1:4$

Answer

$2:1$

Answer

$1:2$

Question 12

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

Accepted Answer

$1:9$

Answer

$1:3$

Answer

$3:1$

Answer

$9:1$

Question 13

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

Accepted Answer

$2.1 	ext{ cm}$

Answer

$3.1 	ext{ cm}$

Answer

$1.5 	ext{ cm}$

Answer

$2.8 	ext{ cm}$

Question 14

Two triangles are similar if their corresponding sides are __________.

Accepted Answer

Proportional

Answer

Equal

Answer

Complementary

Answer

Parallel

Question 15

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

Accepted Answer

$90^{\circ}$

Answer

$120^{\circ}$

Answer

$60^{\circ}$

Answer

$45^{\circ}$

Question 16

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

Accepted Answer

ASA

Answer

SAS

Answer

AAA

Answer

SSS

Question 17

If $	riangle ABC \sim 	riangle EDF$ and $	riangle ABC$ is not similar to $	riangle DEF$, then which of the following is not true?

Accepted Answer

$BC \cdot DE = AB \cdot EF$

Answer

$BC \cdot DF = AC \cdot EF$

Answer

$AB \cdot EF = AC \cdot DE$

Answer

$BC \cdot DE = AB \cdot FD$

Question 18

In $	riangle PQR$, $ST \parallel QR$. If $PS = x$, $SQ = x - 3$, $PT = x + 3$ and $TR = x - 2$, then $x$ is:

Accepted Answer

9

Answer

5

Answer

4

Answer

8

Question 19

If in triangles $ABC$ and $DEF$, $\frac{AB}{DE} = \frac{BC}{FD}$, then they will be similar, when:

Accepted Answer

$\angle B = \angle D$

Answer

$\angle B = \angle E$

Answer

$\angle A = \angle D$

Answer

$\angle A = \angle F$

Question 20

The line segment joining the midpoints of two sides of a triangle is __________ to the third side.

Accepted Answer

Half and Parallel

Answer

Perpendicular

Answer

Parallel

Answer

Equal

Question 21

In $	riangle ABC$, $AD$ is the bisector of $\angle A$. If $AB = 10 	ext{ cm}$, $AC = 14 	ext{ cm}$, and $BC = 6 	ext{ cm}$, find $BD$.

Accepted Answer

$2.5 	ext{ cm}$

Answer

$3.5 	ext{ cm}$

Answer

$2.8 	ext{ cm}$

Answer

$3 	ext{ cm}$

Question 22

XY is parallel to the side BC of $	riangle ABC$ and it divides the triangle into two parts of equal area. Then $AX/AB$ is:

Accepted Answer

$1/\sqrt{2}$

Answer

$1/2$

Answer

$2/1$

Answer

$\sqrt{2}/1$

Question 23

If $	riangle ABC \sim 	riangle DEF$ and $ar(	riangle ABC) = 9 	ext{ cm}^2$, $ar(	riangle DEF) = 64 	ext{ cm}^2$ and $DE = 5.1 	ext{ cm}$, find $AB$.

Accepted Answer

$1.91 	ext{ cm}$

Answer

$2.1 	ext{ cm}$

Answer

$1.5 	ext{ cm}$

Answer

$2.5 	ext{ cm}$

Question 24

In $	riangle ABC$, $\angle A = 90^{\circ}$ and $AD \perp BC$. Then $AD^2$ is equal to:

Accepted Answer

$BD \cdot DC$

Answer

$AB \cdot AC$

Answer

$BD \cdot BC$

Answer

$AB \cdot BC$

Question 25

$O$ is any point inside a rectangle $ABCD$. Then $OB^2 + OD^2$ is equal to:

Accepted Answer

$OA^2 + OC^2$

Answer

$BC^2 + CD^2$

Answer

$AB^2 + BC^2$

Answer

$2OA^2$

Question 26

If $	riangle ABC \sim 	riangle PQR$ and $perimeter(	riangle ABC)/perimeter(	riangle PQR) = 3/4$, and $AB = 6 	ext{ cm}$, find $PQ$.

Accepted Answer

$8 	ext{ cm}$

Answer

$7 	ext{ cm}$

Answer

$9 	ext{ cm}$

Answer

$10 	ext{ cm}$

Question 27

In an equilateral triangle $ABC$, $D$ is a point on side $BC$ such that $BD = \frac{1}{3}BC$. Then $9AD^2$ is:

Accepted Answer

$7AB^2$

Answer

$8AB^2$

Answer

$6AB^2$

Answer

$5AB^2$

Question 28

In $	riangle ABC$, $DE \parallel BC$. If $AD = 4 	ext{ cm}$, $AB = 12 	ext{ cm}$ and $AC = 18 	ext{ cm}$, find $AE$.

Accepted Answer

$6 	ext{ cm}$

Answer

$8 	ext{ cm}$

Answer

$10 	ext{ cm}$

Answer

$12 	ext{ cm}$

Question 29

If sides of two similar triangles are in the ratio $4:9$, then the areas of these triangles are in the ratio:

Accepted Answer

$16:81$

Answer

$2:3$

Answer

$4:9$

Answer

$81:16$

Question 30

In $	riangle ABC$, $D$, $E$, $F$ are midpoints of sides $BC$, $CA$, $AB$ respectively. The ratio of $ar(	riangle DEF)$ to $ar(	riangle ABC)$ is:

Accepted Answer

$1:4$

Answer

$1:2$

Answer

$2:3$

Answer

$4:1$

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

Questions in this Quiz

More Quizzes for Class 10

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

Questions in this Quiz

More Quizzes for Class 10

Biology

Chemistry

Geography

History

Information Technology (402)

Maths

Physics

Political Science