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 9 of 22

1. Q161 CBSE 2025
   The measurements of $△LMN$ ​and $△ABC$ ​are shown ​in ​the figure given ​below. ​The length of side $AC$ is :

   1. (a)$16$ cm
   2. (b)$7$ cm
   3. (c)$8$ cm
   4. (d)$4$ cm
   Show answer

   (c) $8$ cm

   Step-by-step solution →
2. Q162 CBSE 2025
   In $△ABC$, $DE\parallel BC$. ​If $AE=(2x+1)$ cm, $EC=4$ ​cm, $AD=(x+1)$ ​cm and $DB=3$ ​cm, then the ​value of $x$ ​is

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

   (b) $\frac{1}{2}$

   Step-by-step solution →
3. Q163 CBSE 2025
   The perimeters of two similar triangles are $25$ cm ​and $15$ cm respectively. If ​one side of the first ​triangle is $9$ cm, then ​the length of ​the corresponding side of the ​second triangle is:

   1. (a)$5.4$ cm
   2. (b)$6.8$ cm
   3. (c)$2.5$ cm
   4. (d)$4$ cm
   Show answer

   (a) $5.4$ cm

   Step-by-step solution →
4. Q164 CBSE 2025
   A $8$ m high tree casts a $6$ m ​long shadow on the ground. ​At the same ​time, a flag pole casts ​a ​shadow $30$ ​m long on ​the ground. The height of the ​flag pole is

   1. (a)$40$ m
   2. (b)$22.5$ m
   3. (c)$44$ m
   4. (d)$22$ m
   Show answer

   (a) $40$ m

   Step-by-step solution →
5. Q165 CBSE 2025
   If $△ABC\sim △PQR$, $PQ=3AB$ ​and $BC=2$ ​cm, then $QR$ is equal ​to

   1. (a)$2$ cm
   2. (b)$6$ cm
   3. (c)$\frac{2}{3}$ cm
   4. (d)$12$ cm
   Show answer

   (b) $6$ cm

   Step-by-step solution →
6. Q166 CBSE 2025
   ABCD is a ​trapezium with $AB\parallel DC$ ​and ​the diagonals ​intersect at $O$. ​If $AO=(2x+1)$ cm, $OC=(5x-7)$ cm, $DO=(7x-5)$ cm and $OB=(7x+1)$ cm, then ​the value of $x$ ​is:

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

   (a) $2$

   Step-by-step solution →
7. Q167 CBSE 2025
   $PQ$ ​and $PR$ are tangents ​to a circle with centre $O$ ​such that $OQ=QP$. ​The ​value of $\angle OPQ$ ​is equal ​to

   1. (a)$45^{\circ }$
   2. (b)$30^{\circ }$
   3. (c)$60^{\circ }$
   4. (d)$90^{\circ }$
   Show answer

   (a) $45^{\circ }$

   Step-by-step solution →
8. Q168 CBSE 2025
   Line $ST$ is drawn parallel to the ​base $QR$ ​of ​a $\Delta PQR$, meeting $PQ$ at $S$ and $PR$ at $T$. ​If $\frac{PQ}{QS}=3$ ​and $TR=3$ cm, then the length of $PT$ is

   1. (a)$9$ cm
   2. (b)$12$ cm
   3. (c)$6$ cm
   4. (d)$3$ cm
   Show answer

   (c) $6$ cm

   Step-by-step solution →
9. Q169 CBSE 2025
   E ​and F are ​points on the sides AB and ​AC respectively of ​a $△ABC$ such ​that $\frac{AE}{EB}=\frac{AF}{FC}=\frac{1}{2}$. Which ​of the following relation is true?

   1. (a)$EF=2BC$
   2. (b)$BC=2EF$
   3. (c)$EF=3BC$
   4. (d)$BC=3EF$
   Show answer

   (d) $BC=3EF$

   Step-by-step solution →
10. Q170 CBSE 2025
    In ​the ​given figure, in $△ABC$, $AD\perp BC$ and $\angle BAC=90^{\circ }$. ​If $BC=16$ cm and $DC=4$ cm, ​then the value ​of $x$ is :

    1. (a)$4$ cm
    2. (b)$5$ cm
    3. (c)$8$ cm
    4. (d)$3$ cm
    Show answer

    (c) $8$ cm

    Step-by-step solution →
11. Q171 CBSE 2025
    In $△ABC$, $PQ\parallel BC$. ​It is given ​that $AP=2.4$ ​cm, $PB=3.6$ cm and $BC=5.4$ ​cm. $PQ$ ​is equal ​to ​:

    1. (a)$2.7$ cm
    2. (b)$1.8$ cm
    3. (c)$3.6$ cm
    4. (d)$2.16$ cm
    Show answer

    (d) $2.16$ cm

    Step-by-step solution →
12. Q172 CBSE 2025
    Read the ​Assertion ​(A) ​and the Reason (R) ​given ​below and select ​the correct option.

    Assertion (A): In a $△ABC$, D and E are points on the sides AB and AC respectively such that $DE\parallel BC$, then $\frac{AD}{AB}=\frac{AE}{AC}$.

    Reason (R): If a line is drawn parallel to one side of a triangle, intersecting the other two sides, then it divides the two sides in the same ratio.

    1. (a)Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
    2. (b)Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
    3. (c)Assertion (A) is true, but Reason (R) is false.
    4. (d)Assertion (A) is false, but Reason (R) is true.
    Show answer

    (a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).

    Step-by-step solution →
13. Q173 CBSE 2025
    Direction: Read ​the ​Assertion and Reason carefully and choose the correct option: Assertion (A): A ladder leaning against a wall stands at a ​horizontal distance of $6$ m from the wall. If the height ​of ​the ​wall up to which the ladder reaches is $8$ m, then the length of the ladder is $10$ m. Reason (R): The ladder makes an angle of $60^{\circ }$ ​with the ​ground.

    Assertion (A): A ladder leaning against a wall stands at a horizontal distance of $6$ m from the wall. If the height of the wall up to which the ladder reaches is $8$ m, then the length of the ladder is $10$ m.

    Reason (R): The ladder makes an angle of $60^{\circ }$ with the ground.

    1. (a)Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
    2. (b)Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).
    3. (c)Assertion (A) is true, but Reason (R) is false.
    4. (d)Assertion (A) is false, but Reason (R) is true.
    Show answer

    (c) Assertion (A) is true, but Reason (R) is false.

    Step-by-step solution →
14. Q174 CBSE 2025
    Statements of ​Assertion (A) ​and ​Reason (R) are given. ​Choose the correct ​option.

    Assertion (A): If two triangles are equiangular, then they are similar.

    Reason (R): If two triangles are similar, then they are congruent.

    1. (a)Both A and R are true and R is the correct explanation of A.
    2. (b)Both A and R are true but R is not the correct explanation of A.
    3. (c)A is true but R is false.
    4. (d)A is false but R is true.
    Show answer

    (c) A is true but R is false.

    Step-by-step solution →
15. Q175 CBSE 2025
    Assertion (A): All congruent triangles are similar.

    Reason (R): In congruent triangles, the ratio of corresponding sides is $1:1$.

    1. (a)Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
    2. (b)Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
    3. (c)Assertion (A) is true, but Reason (R) is false.
    4. (d)Assertion (A) is false, but Reason (R) is true.
    Show answer

    (a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).

    Step-by-step solution →
16. Q176 CBSE 2025
    Assertion (A): $△ABC\sim △PQR$ such ​that $\angle A=65^{\circ }$, $\angle C=60^{\circ }$. Hence $\angle Q=55^{\circ }$. Reason (R): ​The ​sum ​of ​all angles of a triangle is $180^{\circ }$. Choose the correct ​option.

    Assertion (A): $△ABC\sim △PQR$ with $\angle A=65^{\circ },\angle C=60^{\circ }$. Hence $\angle Q=55^{\circ }$.

    Reason (R): The sum of all angles of a triangle is $180^{\circ }$.

    1. (a)Both A and R are true, and R is the correct explanation of A.
    2. (b)Both A and R are true, but R is not the correct explanation of A.
    3. (c)A is true but R is false.
    4. (d)A is false but R is true.
    Show answer

    (b) Both A and R are true, but R is not the correct explanation of A.

    Step-by-step solution →
17. Q177 CBSE 2025
    In the given figure, $Z$ ​is ​a point on the side $BC$ ​of $△ABC$ ​such that $XZ\parallel AB$ and $YZ\parallel AC$. If $XY$ and $CB$ produced meet at $O$, ​then ​prove ​that $Z{O}^2=OB\times OC$.

    Show answer

    Hence proved: $Z{O}^2=OB\times OC$.

    Step-by-step solution →
18. Q178 CBSE 2025
    $S$ and $T$ are ​points on sides $PR$ and $QR$ ​of $△PQR$ ​such ​that $\angle P=\angle RTS$. ​Show ​that $△RPQ\sim △RTS$.
    Show answer

    $△RPQ\sim △RTS$ by the AA similarity criterion ($\angle R$ common and $\angle RPQ=\angle RTS$), with $R\leftrightarrow R$, $P\leftrightarrow T$, $Q\leftrightarrow S$. Hence proved.

    Step-by-step solution →
19. Q179 CBSE 2025
    If ​a ​line ​intersects ​sides $AB$ and $AC$ of $△ABC$ at $D$ and $E$ respectively, ​and ​is parallel to $BC$, ​prove that $\frac{AD}{AB}=\frac{AE}{AC}$.
    Show answer

    $\frac{AD}{AB}=\frac{\text{ar}(△ADE)}{\text{ar}(△ABE)}=\frac{\text{ar}(△ADE)}{\text{ar}(△ADC)}=\frac{AE}{AC}$, because $\text{ar}(△ABE)=\text{ar}(△ADC)$ when $DE\parallel BC$. Hence proved.

    Step-by-step solution →
20. Q180 CBSE 2025
    $D$ ​is ​a point ​on ​side $BC$ ​of $△ABC$ ​such ​that $\angle ADC=\angle BAC$. Prove that $(CA{)}^2=CB\cdot CD$.
    Show answer

    Since $\angle ADC=\angle BAC$ and $\angle C$ is common, $△ADC\sim △BAC$ (AA). Hence $\frac{CD}{CA}=\frac{CA}{CB}$, so $(CA{)}^2=CB\cdot CD$. Hence proved.

    Step-by-step solution →