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 6 of 22

1. Q101 CBSE 2026
   Two isosceles triangles :

   1. (a)are always similar, but not congruent.
   2. (b)are always congruent, but not similar.
   3. (c)may or may not be similar.
   4. (d)are always similar and congruent.
   Show answer

   (c) may or may not be similar.

   Step-by-step solution →
2. Q102 CBSE 2026
   If ​in ​two triangles $ABC$ and $DEF$, $\frac{AB}{EF}=\frac{BC}{DE}=\frac{CA}{DF}$; ​then

   1. (a)$△DEF\sim △BCA$
   2. (b)$△DEF\sim △CBA$
   3. (c)$△ABC\sim △DEF$
   4. (d)$△ABC\sim △DFE$
   Show answer

   (b) $△DEF\sim △CBA$

   Step-by-step solution →
3. Q103 CBSE 2026
   In ​the adjoining ​figure, ​if $EA\parallel SR$ and $PE=x$ ​cm, then the value of $5x$ is :

   1. (a)$2.4$ cm
   2. (b)$12$ cm
   3. (c)$1.35$ cm
   4. (d)$6.75$ cm
   Show answer

   (b) $12$ cm

   Step-by-step solution →
4. Q104 CBSE 2026
   In $△ABC$, $P$ is a point on $AB$ and $Q$ is ​a ​point on $AC$ ​such ​that $PQ\parallel BC$. If $AP:PB=3:2$, then $PQ:BC$ is ​equal to:

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

   (c) $3:5$

   Step-by-step solution →
5. Q105 CBSE 2026
   In ​the ​given ​figure, $DE\parallel BC$. If $AD:AB=1:3$ ​and $AE=2.5$ ​cm, then $AC$ equals

   1. (a)$7.5$ cm
   2. (b)$5$ cm
   3. (c)$10$ cm
   4. (d)$2.5$ cm
   Show answer

   (a) $7.5$ cm

   Step-by-step solution →
6. Q106 CBSE 2026
   If ​in ​a $△ABC$, $AB=6$ cm ​and $DE\parallel BC$ such ​that $AE=\frac{1}{3}AC$, ​then ​the length ​of $BD$ is

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

   (c) $4$ cm

   Step-by-step solution →
7. Q107 CBSE 2026
   It is given ​that $△ABC\sim △QRP$ such that $AB=9$ ​cm, $BC=5$ cm and $PR=2$ cm. ​Length of ​side $QR$ is ​:

   1. (a)$0.9$ cm
   2. (b)$\frac{5}{18}$ cm
   3. (c)$\frac{10}{9}$ cm
   4. (d)$3.6$ cm
   Show answer

   (d) $3.6$ cm

   Step-by-step solution →
8. Q108 CBSE 2026
   In ​the given ​figure, $PQ\parallel YZ$ ​such ​that $XP:PY=2:3$. If $PQ=5$ ​cm, then $YZ$ ​equals

   1. (a)$12.5$ cm
   2. (b)$10$ cm
   3. (c)$15$ cm
   4. (d)$7.5$ cm
   Show answer

   (a) $12.5$ cm

   Step-by-step solution →
9. Q109 CBSE 2026
   In ​the given ​figure, $PQ\parallel BC$. ​If $AP:AB=3:7$, then $AQ:QC$ equals:

   1. (a)$3:7$
   2. (b)$3:10$
   3. (c)$7:3$
   4. (d)$3:4$
   Show answer

   (d) $3:4$

   Step-by-step solution →
10. Q110 CBSE 2026
    $D$ ​is ​a ​point on ​the ​side $BC$ ​of $△ABC$ such that $\angle CAB=\angle CDA$. ​Show that $C{A}^2=CB\times CD$.

    Show answer

    Since $\angle C$ is common to $△CAB$ and $△CDA$ and $\angle CAB=\angle CDA$, by AA similarity $△CAB\sim △CDA$. Hence $\frac{CA}{CD}=\frac{CB}{CA}$, which gives $C{A}^2=CB\times CD$. Hence proved.

    Step-by-step solution →
11. Q111 CBSE 2026
    In $△ABC$, $DE\parallel BC$. ​If $AD=x$, $DB=x-2$, $AE=x+2$ ​and $EC=x-1$, then ​find the value ​of $x$.
    Show answer

    The value of $x$ is $4$.

    Step-by-step solution →
12. Q112 CBSE 2026
    In ​the given ​figure, $△AHK\sim △ABC$. If $AK=10$ cm, $BC=3.5$ ​cm and $HK=7$ ​cm, find ​the ​length of $AC$.

    Show answer

    The length of $AC$ is $5$ cm.

    Step-by-step solution →
13. Q113 CBSE 2026
    In ​the ​figure ​given ​above, $△ABC\sim △XYZ$, ​then find the ​values of $x$ and $y$.

    Show answer

    The values are $x=4.8$ cm and $y=5$ cm.

    Step-by-step solution →
14. Q114 CBSE 2026
    In the ​given ​figure, $XY\parallel QR$, $\frac{PQ}{XQ}=\frac{7}{3}$ ​and $PR=6.3$ ​cm. Find ​the length of $YR$.

    Show answer

    The length of $YR$ is $2.7$ cm.

    Step-by-step solution →
15. Q115 CBSE 2026
    In ​the given figure, $AB\parallel DE$ ​and $AC\parallel DF$. Show ​that $△ABC\sim △DEF$. If $BC=10$ cm, $EB=CF=5$ cm and $AB=7$ cm, ​then ​find the length $DE$.

    Show answer

    $△ABC\sim △DEF$ by the AA criterion, and $DE=14$ cm.

    Step-by-step solution →
16. Q116 CBSE 2026
    In ​the adjoining ​figure, $AP=\frac{1}{2}AB$ and $PQ\parallel BC$. If $CQ=3$ cm, ​then find ​the length ​of $AC$.

    Show answer

    The length of $AC$ is $6$ cm.

    Step-by-step solution →
17. Q117 CBSE 2026
    In ​the figure ​given ​below, $\angle 1=\angle 2$ ​and $\frac{BE}{BC}=\frac{CD}{AB}$. Prove ​that $△BDE\sim △BAC$.

    Show answer

    Since $\angle 1=\angle 2$, in triangle $BDC$ the sides opposite these equal angles are equal, so $BD=CD$. Substituting in $\frac{BE}{BC}=\frac{CD}{AB}$ gives $\frac{BD}{BA}=\frac{BE}{BC}$, and with the common included angle $\angle DBE=\angle ABC$, the SAS similarity criterion gives $△BDE\sim △BAC$. Hence proved.

    Step-by-step solution →
18. Q118 CBSE 2026
    Two chords $AB$ and $CD$ intersect ​each other ​at the point $E$ as ​shown in ​the ​given ​figure. Prove ​that $△AED\sim △CEB$.

    Show answer

    In $△AED$ and $△CEB$ : $\angle AED=\angle CEB$ (vertically opposite angles) and $\angle ADE=\angle CBE$ (angles in the same segment on chord $AC$), so by the AA similarity criterion $△AED\sim △CEB$

    Step-by-step solution →
19. Q119 CBSE 2026
    In ​the given ​figure, $△PQR$ ​is a right ​triangle, right-angled at $Q$ ​and $QS\perp PR$. Prove ​that $△PQS\sim △QRS$.

    Show answer

    In $△PQS$ and $△QRS$ : $\angle PSQ=\angle QSR=90^{\circ }$ and $\angle QPS=\angle SQR$ (each is complementary to $\angle PQS$), so by the AA similarity criterion $△PQS\sim △QRS$. Hence proved in either alternative.

    Step-by-step solution →
20. Q120 CBSE 2026
    The ​diagonals of ​a quadrilateral $ABCD$ ​intersect each other at ​the ​point $O$ such ​that $\frac{AO}{OC}=\frac{BO}{OD}$. Show that ​quadrilateral $ABCD$ is a trapezium.
    Show answer

    Since $AB\parallel DC$, quadrilateral $ABCD$ has a pair of parallel sides and is therefore a trapezium. Hence proved.

    Step-by-step solution →