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 13 of 22

1. Q241 CBSE 2024
   It ​is ​given ​that $△ABC\sim △DEF$. If $\angle A=55^{\circ },\angle E=45^{\circ }$, ​then $\angle C$ is :

   1. (a)80 degrees
   2. (b)90 degrees
   3. (c)55 degrees
   4. (d)45 degrees
   Show answer

   (a) 80 degrees

   Step-by-step solution →
2. Q242 CBSE 2024
   In a $△ABC$, a ​line DE is drawn parallel to ​BC to ​intersect AB at D and AC at ​E. If $AD=2$ cm, $BD=3$ ​cm ​and $DE=4$ cm, then the ​length of BC (in ​cm) is:

   1. (a)$6$
   2. (b)$10$
   3. (c)$\frac{8}{3}$
   4. (d)$\frac{20}{3}$
   Show answer

   (b) $10$

   Step-by-step solution →
3. Q243 CBSE 2024
   In ​the ​given figure, in $△ABC$, $DE\parallel BC$. If $AD=2x$ ​cm, $AE=(x+2)$ cm, $DB=4$ cm, $EC=3$ ​cm, ​then the ​value of $x$ ​is ​:

   1. (a)3
   2. (b)2
   3. (c)6
   4. (d)4
   Show answer

   (d) 4

   Step-by-step solution →
4. Q244 CBSE 2024
   If a ​vertical pole of ​length $7.5$ m casts a shadow $5$ m ​long ​on the ​ground and at the same ​time, a tower casts a shadow $24$ m ​long, then the height of the tower is :

   1. (a)$20$ m
   2. (b)$40$ m
   3. (c)$60$ m
   4. (d)$36$ m
   Show answer

   (d) $36$ m

   Step-by-step solution →
5. Q245 CBSE 2024
   In the given ​figure, if $△ABC\sim △QPR$, then ​the ​value ​of x ​is :

   1. (a)5.3 cm
   2. (b)4.6 cm
   3. (c)2.3 cm
   4. (d)4 cm
   Show answer

   (c) 2.3 cm

   Step-by-step solution →
6. Q246 CBSE 2024
   Assertion (A): $ABCD$ is a trapezium with $DC\parallel AB$. $E$ and $F$ are points on $AD$ and $BC$ respectively, such that $EF\parallel AB$. Then $\frac{AE}{ED}=\frac{BF}{FC}$.

   Reason (R): Any line parallel to parallel sides of a trapezium divides the non-parallel sides proportionally.

   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

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

   Step-by-step solution →
7. Q247 CBSE 2024
   Directions: A statement of Assertion (A) ​is ​followed ​by ​a ​statement of Reason (R). Choose ​the ​correct option.

   Assertion (A): A line drawn parallel to any one side of a triangle intersects the other two sides in the same ratio.

   Reason (R): Parallel lines cannot be drawn to any side of a triangle.

   1. (a)Both Assertion (A) and Reason (R) are correct and Reason (R) is the correct explanation of Assertion (A).
   2. (b)Both Assertion (A) and Reason (R) are correct 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 →
8. Q248 CBSE 2024
   $D$ ​is a ​point ​on ​the side $BC$ of $△ABC$ ​such that $\angle ADC=\angle BAC$. ​Show that $A{C}^2=BC\times DC$.

   Show answer

   Since $\angle ADC=\angle BAC$ (given) and $\angle ACD=\angle BCA$ (common), $△ADC\sim △BAC$ by AA similarity. Hence $\frac{DC}{AC}=\frac{AC}{BC}$, so $A{C}^2=BC\times DC$. Hence proved.

   Step-by-step solution →
9. Q249 CBSE 2024
   E and F are points on the ​sides ​PQ and PR ​respectively of a $△PQR$. If $PE=3.9$ ​cm, $EQ=3$ cm, $PF=3.6$ ​cm and $PR=6$ cm, find whether $EF\parallel QR$.
   Show answer

   $EF$ is **not** parallel to $QR$, because $\frac{PE}{EQ}=1.3$ while $\frac{PF}{FR}=1.5$, and a line parallel to $QR$ would make these equal.

   Step-by-step solution →
10. Q250 CBSE 2024
    PQRS ​is ​a trapezium with $PQ\parallel SR$. If M and N are two points on the ​non-parallel sides ​PS and QR ​respectively, such ​that MN is parallel to PQ, then ​show that $\frac{PM}{MS}=\frac{QN}{NR}$.

    Show answer

    Hence proved: $\frac{PM}{MS}=\frac{QN}{NR}$, since both ratios equal $\frac{PO}{OR}$, where $O$ is the point where the diagonal $PR$ meets $MN$.

    Step-by-step solution →
11. Q251 CBSE 2024
    E and F ​are points on the sides PQ and ​PR respectively of ​a $△PQR$ and $EF\parallel QR$. ​If $PE=2.5$ cm, $PQ=6$ cm ​and $PF=4.5$ cm, ​find ​the lengths ​of $RF$ and $PR$.
    Show answer

    $RF=6.3$ cm and $PR=10.8$ cm.

    Step-by-step solution →
12. Q252 CBSE 2024
    In ​the given ​figure, ABC is ​a ​triangle in ​which $DE\parallel BC$, $AD=3$ cm, $BD=4$ cm and $AC=14$ cm. Find ​the length of $AE$.

    Show answer

    $AE=6$ cm.

    Step-by-step solution →
13. Q253 CBSE 2024
    In ​a $△ABC$, ​D and E ​are points ​on the sides AB and AC ​respectively such that $BD=CE$. If $\angle B=\angle C$, then show that $DE\parallel BC$.
    Show answer

    Since $\angle B=\angle C$, $AB=AC$. With $BD=CE$ this gives $AD=AB-BD=AC-CE=AE$, so $\frac{AD}{DB}=\frac{AE}{EC}$, and by the converse of the Basic Proportionality Theorem $DE\parallel BC$. Hence proved.

    Step-by-step solution →
14. Q254 CBSE 2024
    If $△ABC\sim △DEF$ ​and $AB=4$ ​cm, $DE=6$ cm, $EF=9$ cm and $FD=12$ ​cm, ​find the ​perimeter of $△ABC$.
    Show answer

    The perimeter of $△ABC$ is $18$ cm.

    Step-by-step solution →
15. Q255 CBSE 2024
    In the ​given figure, ​PQR is a ​triangle ​in ​which PS and QT ​are altitudes from P and Q respectively, intersecting each ​other at ​M. Prove that $△QSM\sim △PTM$.

    Show answer

    $△QSM\sim △PTM$ by the AA similarity criterion, with $Q\leftrightarrow P$, $S\leftrightarrow T$ and $M\leftrightarrow M$. Hence proved.

    Step-by-step solution →
16. Q256 CBSE 2024
    In ​the ​given ​figure, PQ ​|| RS. ​Prove ​that $OP\times OR=OQ\times OS$.

    Show answer

    Since $△OPQ\sim △OSR$ (AA), $\frac{OP}{OS}=\frac{OQ}{OR}$, so $OP\times OR=OQ\times OS$. Hence proved.

    Step-by-step solution →
17. Q257 CBSE 2024
    In ​the given figure, LM ​|| CB ​and ​LN ​|| CD. ​Prove that $\frac{AM}{AN}=\frac{AB}{AD}$.

    Show answer

    $\frac{AM}{AN}=\frac{AB}{AD}$. Hence proved.

    Step-by-step solution →
18. Q258 CBSE 2024
    In the ​given figure, $\frac{EA}{EC}=\frac{EB}{ED}$, ​prove that $△EAB\sim △ECD$.

    Show answer

    Since $\angle AEB=\angle CED$ (vertically opposite angles) and $\frac{EA}{EC}=\frac{EB}{ED}$ (given), the sides including the equal angles are proportional, so $△EAB\sim △ECD$ by the SAS similarity criterion. Hence proved.

    Step-by-step solution →
19. Q259 CBSE 2024
    A line $l$ intersects ​sides $PQ$ and $PR$ ​of $△PQR$ ​at $L$ and $M$ respectively such ​that $LM\parallel QR$. If $PQ=12$ ​cm, $PR=10$ cm ​and $PL=7.2$ cm, then find the length of $PM$.
    Show answer

    $PM=6$ cm

    Step-by-step solution →
20. Q260 CBSE 2024
    In ​the given figure, $ABCD$ is a quadrilateral. ​Diagonal $BD$ ​bisects $\angle B$ and $\angle D$ ​both. Prove ​that ​: ​

    1. (i)$△ABD\sim △CBD$
    2. (ii)$AB=BC$

    Show answer

    (i) $△ABD\sim △CBD$ by the AA criterion, since $\angle ABD=\angle CBD$ and $\angle ADB=\angle CDB$; (ii) The ratio $\frac{AB}{CB}=\frac{BD}{BD}=1$, so $AB=BC$. Hence proved.

    Step-by-step solution →