Class 10 Maths · Chapter 6

Triangles

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

CBSE Class 10 Maths previous year papers, with answers →

Questions · page 4 of 6

1. Q61 CBSE 2026
   Observe the ​given ​triangles : Which of the ​following ​statements is ​true ​?

   1. (a)$△LMN\sim △ABC$
   2. (b)$△LMN\sim △ACB$
   3. (c)$△NML\sim △ABC$
   4. (d)$△NML\sim △ACB$
   Show answer

   (c) $△NML\sim △ABC$

   Step-by-step solution →
2. Q62 CBSE 2026
   In ​triangles $ABC$ ​and $PQR$, $\angle A=\angle Q$ ​and $\angle B=\angle R$, ​then $AB:AC$ is ​equal ​to ​:

   1. (a)$PQ:PR$
   2. (b)$PQ:QR$
   3. (c)$QR:QP$
   4. (d)$PR:QR$
   Show answer

   (c) $QR:QP$

   Step-by-step solution →
3. Q63 CBSE 2026
   If $△DEF\sim △PQR$ such ​that $3DE=PQ$ ​and $EF=6$ ​cm, ​then ​the length of $QR$ ​is :

   1. (a)$12\text{cm}$
   2. (b)$3\text{cm}$
   3. (c)$2\text{cm}$
   4. (d)$18\text{cm}$
   Show answer

   (d) $18\text{cm}$

   Step-by-step solution →
4. Q64 CBSE 2026
   If $△ABC\sim △ADE$ ​in ​the adjoining ​figure, then which of the following ​is ​true ?

   1. (a)$\frac{AB}{BE}=\frac{AC}{CD}$
   2. (b)$\frac{AB}{AD}=\frac{AC}{AE}$
   3. (c)$\frac{AB}{BC}=\frac{AE}{DE}$
   4. (d)$\frac{AC}{AD}=\frac{AB}{AE}$
   Show answer

   (b) $\frac{AB}{AD}=\frac{AC}{AE}$

   Step-by-step solution →
5. Q65 CBSE 2026
   In ​the ​given ​figure, ​if $△ACP\sim △DCP$, then :

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

   (b) $\angle DCP=30^{\circ }$

   Step-by-step solution →
6. Q66 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 →
7. Q67 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 →
8. Q68 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 →
9. Q69 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 →
10. Q70 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 →
11. Q71 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 →
12. Q72 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 →
13. Q73 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 →
14. Q74 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 →
15. Q75 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 →
16. Q76 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 →
17. Q77 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 →
18. Q78 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 →
19. Q79 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 →
20. Q80 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 →