Class 10 Maths · Chapter 6

Triangles

424 Class 10 Maths questions on Triangles from the NCERT textbook, NCERT Exemplar and CBSE board papers 2018–2026, each with its answer and a step-by-step solution.

CBSE Class 10 Maths previous year papers, with answers →

Questions · page 16 of 22

1. Q301 CBSE 2023
   If $△ABC\sim △DEF$, $AB=6$ cm, $DE=9$ ​cm, $EF=6$ ​cm and $FD=12$ ​cm, ​then the perimeter of $△ABC$ ​is ​:

   1. (a)$28$ cm
   2. (b)$28.5$ cm
   3. (c)$18$ cm
   4. (d)$23$ cm
   Show answer

   (c) $18$ cm

   Step-by-step solution →
2. Q302 CBSE 2023
   In the given ​figure, $DE\parallel BC$. ​If $AD=3$ ​cm, $AB=7$ ​cm ​and $EC=3$ cm, ​then the ​length of $AE$ is

   1. (a)2 cm
   2. (b)2.25 cm
   3. (c)3.5 cm
   4. (d)4 cm
   Show answer

   (b) 2.25 cm

   Step-by-step solution →
3. Q303 CBSE 2023
   A ​vertical pole 10 ​m ​long casts a shadow of length 5 m ​on the ground. At the same time, ​a tower casts ​a shadow of length 12.5 m on the ground. The height ​of the ​tower is :

   1. (a)20 m
   2. (b)22 m
   3. (c)25 m
   4. (d)24 m
   Show answer

   (c) 25 m

   Step-by-step solution →
4. Q304 CBSE 2023
   In ​the ​given figure, $△ABC\sim △QPR$. ​If $AC=6$ cm, $BC=5$ cm, $QR=3$ cm ​and $PR=x$; ​then the ​value ​of $x$ is :

   1. (a)$3.6$ cm
   2. (b)$2.5$ cm
   3. (c)$10$ cm
   4. (d)$3.2$ cm
   Show answer

   (b) $2.5$ cm

   Step-by-step solution →
5. Q305 CBSE 2023
   In the ​given figure, $DE\parallel BC$. If $AD=2$ ​units, $DB=AE=3$ units ​and $EC=x$ units, ​then the value ​of $x$ ​is:

   1. (a)$2$
   2. (b)$3$
   3. (c)$5$
   4. (d)$\frac{9}{2}$
   Show answer

   (d) $\frac{9}{2}$

   Step-by-step solution →
6. Q306 CBSE 2023
   In ​the given figure, $AD=2$ cm, $DB=3$ cm, $DE=2.5$ cm ​and $DE\parallel BC$. ​The value ​of $x$ is :

   1. (a)6 cm
   2. (b)$3.75$ cm
   3. (c)$6.25$ cm
   4. (d)$7.5$ cm
   Show answer

   (c) $6.25$ cm

   Step-by-step solution →
7. Q307 CBSE 2023
   In $△ABC$ ​and $△DEF$, $\frac{AB}{DE}=\frac{BC}{FD}$. ​Which of the following ​makes ​the ​two triangles ​similar ?

   1. (a)$\angle A=\angle D$
   2. (b)$\angle B=\angle D$
   3. (c)$\angle B=\angle E$
   4. (d)$\angle A=\angle F$
   Show answer

   (b) $\angle B=\angle D$

   Step-by-step solution →
8. Q308 CBSE 2023
   In ​the figure, the ​criterion ​of similarity ​by which $△ABC\sim △PQR$ ​is:

   1. (a)SSA (Side - Side - Angle) Similarity
   2. (b)ASA (Angle - Side - Angle) Similarity
   3. (c)SAS (Side - Angle - Side) Similarity
   4. (d)AA (Angle - Angle) Similarity
   Show answer

   (c) SAS (Side - Angle - Side) Similarity

   Step-by-step solution →
9. Q309 CBSE 2023
   In $△ABC$, $PQ\parallel BC$. If $PB=6$ ​cm, $AP=4$ ​cm, $AQ=8$ ​cm, find the ​length of $AC$.

   1. (a)$12$ cm
   2. (b)$20$ cm
   3. (c)$6$ cm
   4. (d)$14$ cm
   Show answer

   (b) $20$ cm

   Step-by-step solution →
10. Q310 CBSE 2023
    In $△ABC$, $DE\parallel BC$. ​If $AD:DB=2:3$, ​then $DE:BC$ ​is equal ​to:

    1. (a)$2:3$
    2. (b)$3:5$
    3. (c)$2:5$
    4. (d)$3:2$
    Show answer

    (c) $2:5$

    Step-by-step solution →
11. Q311 CBSE 2023
    In two ​triangles $△PQR$ ​and $△ABC$, it is ​given that $\frac{AB}{BC}=\frac{PQ}{PR}$. For these two ​triangles ​to be similar, which of the following should be ​true ​?

    1. (a)$\angle A=\angle P$
    2. (b)$\angle B=\angle Q$
    3. (c)$\angle B=\angle P$
    4. (d)$CA=QR$
    Show answer

    (c) $\angle B=\angle P$

    Step-by-step solution →
12. Q312 CBSE 2023
    In ​the given figure, $AB\parallel PQ$. ​If $AB=6$ cm, $PQ=2$ cm ​and $OB=3$ ​cm, ​then ​the ​length of $OP$ is:

    1. (a)$9$ cm
    2. (b)$3$ cm
    3. (c)$4$ cm
    4. (d)$1$ cm
    Show answer

    (d) $1$ cm

    Step-by-step solution →
13. Q313 CBSE 2023
    In the ​given ​figure, $DE\parallel AC$ ​and $\frac{BE}{EC}=\frac{BC}{CP}$. ​Prove that $DC\parallel AP$.

    Show answer

    Since $\frac{BD}{DA}=\frac{BE}{EC}=\frac{BC}{CP}$, by the converse of BPT $DC\parallel AP$. Hence proved.

    Step-by-step solution →
14. Q314 CBSE 2023
    A vertical ​pole ​30 ​m high ​casts a shadow 15 m long ​on the ground. ​At the same ​time, a tower casts a shadow 70 m long on the ground. Find the height of the tower.
    Show answer

    140 m

    Step-by-step solution →
15. Q315 CBSE 2023
    In the ​given ​figure, $XZ$ is parallel to $BC$. $AZ=3$ ​cm, $ZC=2$ ​cm, $BM=3$ ​cm and $MC=5$ cm. ​Find ​the length of $XY$.

    Show answer

    $XY=\frac{9}{5}=1.8$ cm

    Step-by-step solution →
16. Q316 CBSE 2023
    P and Q are respectively the ​points ​on ​the ​sides ​AB and AC of a triangle ABC such ​that $AB=12.5$ cm, $AP=5$ cm and $CQ=6$ cm. If $PQ\parallel BC$, then find the ​length of AQ.
    Show answer

    $AQ=4$ cm

    Step-by-step solution →
17. Q317 CBSE 2023
    In ​the figure, ​E is a ​point ​on side ​CB produced of ​an isosceles triangle ABC with $AB=AC$. If $AD\perp BC$ and $EF\perp AC$, ​prove that $△ABD\sim △ECF$.

    Show answer

    $△ABD\sim △ECF$ by the AA similarity criterion.

    Step-by-step solution →
18. Q318 CBSE 2023
    In ​the given figure, $ABC$ and $AMP$ ​are two ​right triangles, right ​angled ​at $B$ and $M$, respectively. Prove that $△ABC\sim △AMP$.

    Show answer

    $△ABC\sim △AMP$ by the AA criterion.

    Step-by-step solution →
19. Q319 CBSE 2023
    In ​the ​adjoining figure, $A$, $B$ and $C$ are ​points on $OP$, $OQ$ and $OR$ respectively ​such ​that $AB\parallel PQ$ ​and $AC\parallel PR$. Show that $BC\parallel QR$.

    Show answer

    $BC\parallel QR$ (proved using BPT and its converse).

    Step-by-step solution →
20. Q320 CBSE 2023
    In the ​given ​figure, ABC is ​a triangle in ​which $DE\parallel BC$. ​If $AD=x$, $DB=x-2$, $AE=x+2$ and $EC=x-1$, ​then ​find ​the value of $x$.

    Show answer

    $x=4$

    Step-by-step solution →