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 3 of 6

1. Q41 Exemplar · Exercise 6.3
   Diagonals of a trapezium ​PQRS ​intersect each ​other at ​the point O, PQ $\parallel$ RS ​and PQ = ​3 RS. Find the ratio of the areas of triangles POQ and ROS.
   Show answer

   The ratio of the areas of triangles POQ and ROS is $9:1$.

   Step-by-step solution →
2. Q42 Exemplar · Exercise 6.3
   In Fig. 6.10, ​if $AB\parallel DC$ ​and AC and PQ ​intersect ​each other at ​the point ​O, prove that $OA\cdot CQ=OC\cdot AP$.

   Show answer

   Proved: $AB\parallel DC$ gives $△OAP\sim △OCQ$ (AA), so $\frac{OA}{OC}=\frac{AP}{CQ}$, hence $OA\cdot CQ=OC\cdot AP$.

   Step-by-step solution →
3. Q43 Exemplar · Exercise 6.3
   Find ​the ​altitude of ​an ​equilateral ​triangle of side 8 ​cm.
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   The altitude of the equilateral triangle is $4\sqrt{3}$ cm, approximately 6.93 cm.

   Step-by-step solution →
4. Q44 Exemplar · Exercise 6.3
   If $△ABC\sim △DEF$, $AB=4$ cm, $DE=6$ ​cm, $EF=9$ cm ​and $FD=12$ ​cm, ​find the ​perimeter of $△ABC$.
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   The perimeter of $△ABC$ is $18$ cm.

   Step-by-step solution →
5. Q45 Exemplar · Exercise 6.3
   In ​Fig. 6.11, if ​DE $\parallel$ BC, find ​the ​ratio of ​ar (ADE) and ​ar ​(DECB).

   Show answer

   $ar(△ADE):ar(DECB)=1:3$.

   Step-by-step solution →
6. Q46 Exemplar · Exercise 6.3
   ABCD is a ​trapezium ​in which $AB\parallel DC$ and P and Q are ​points on AD and BC, ​respectively such that $PQ\parallel DC$. ​If $PD=18$ ​cm, $BQ=35$ cm ​and $QC=15$ cm, find AD.
   Show answer

   $AD=60$ cm.

   Step-by-step solution →
7. Q47 Exemplar · Exercise 6.3
   Corresponding sides of two ​similar triangles ​are in the ratio ​of $2:3$. ​If ​the area of the smaller triangle is $48$ cm${}^2$, find ​the area of ​the larger triangle.
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   The area of the larger triangle is $108$ cm${}^2$.

   Step-by-step solution →
8. Q48 Exemplar · Exercise 6.3
   In a ​triangle ​PQR, N ​is a point ​on ​PR such that QN is perpendicular to ​PR. If PN.NR = QN^2, ​prove that ​angle PQR = 90 degrees.
   Show answer

   $\angle PQR=90^{\circ }$, proved using SAS similarity of triangles PNQ and QNR.

   Step-by-step solution →
9. Q49 Exemplar · Exercise 6.3
   Areas of two similar triangles ​are ​36 cm${}^2$ ​and 100 cm${}^2$. If the length of a side of ​the larger triangle is 20 cm, find the length ​of the corresponding side ​of the smaller triangle.
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   The corresponding side of the smaller triangle is $12$ cm.

   Step-by-step solution →
10. Q50 Exemplar · Exercise 6.3
    In ​Fig. ​6.12, ​if $\angle ACB=\angle CDA$, $AC=8$ cm ​and $AD=3$ ​cm, find ​BD.

    Show answer

    BD = 55/3 cm, approximately 18.33 cm.

    Step-by-step solution →
11. Q51 Exemplar · Exercise 6.3
    A 15 metres high tower casts a shadow 24 metres long ​at a certain time ​and at the same time, a telephone pole casts ​a ​shadow 16 metres long. Find ​the ​height of the telephone pole.
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    The telephone pole is $10$ metres high.

    Step-by-step solution →
12. Q52 Exemplar · Exercise 6.3
    Foot of a 10 m ​long ladder leaning against a vertical wall is 6 m ​away ​from the base of the wall. Find ​the height of ​the ​point on ​the wall where the top of ​the ladder reaches.
    Show answer

    The top of the ladder reaches a height of $8$ m on the wall.

    Step-by-step solution →
13. Q53 CBSE 2026
    It is given ​that $△ABC\sim △EDF$. ​Which of ​the following is ​not true ​?

    1. (a)$\frac{\text{Perimeter of }△ABC}{\text{Perimeter of }△EDF}=\frac{AB}{ED}$
    2. (b)$\frac{AB}{ED}=\frac{AC}{EF}$
    3. (c)$\angle A=\angle D,\angle C=\angle F$
    4. (d)$\frac{AB+BC}{AC}=\frac{DE+DF}{EF}$
    Show answer

    (c) $\angle A=\angle D,\angle C=\angle F$

    Step-by-step solution →
14. Q54 CBSE 2026
    In $△DEF$, $AB\parallel EF$. The ​value ​of $x$ is ​:

    1. (a)$0,2$
    2. (b)$2$ only
    3. (c)$-2$
    4. (d)$1$
    Show answer

    (b) $2$ only

    Step-by-step solution →
15. Q55 CBSE 2026
    Which of ​the following statements ​is ​not ​always ​true?

    1. (a)Two circles are similar.
    2. (b)Two isosceles right triangles are similar.
    3. (c)Two rectangles are similar.
    4. (d)Two equilateral triangles are similar.
    Show answer

    (c) Two rectangles are similar.

    Step-by-step solution →
16. Q56 CBSE 2026
    Devansh proved that $△ABC\sim △PQR$ using SAS ​similarity criteria. ​If ​he ​found $\angle C=\angle R$, ​then which ​of the following was proved true?

    1. (a)$\frac{AC}{AB}=\frac{PR}{PQ}$
    2. (b)$\frac{BC}{AC}=\frac{PR}{QR}$
    3. (c)$\frac{AC}{BC}=\frac{PR}{PQ}$
    4. (d)$\frac{AC}{BC}=\frac{PR}{QR}$
    Show answer

    (d) $\frac{AC}{BC}=\frac{PR}{QR}$

    Step-by-step solution →
17. Q57 CBSE 2026
    In ​the ​given figure, $DE\parallel BC$. ​If $\frac{AD}{DB}=\frac{1}{3}$ ​and $AC=6$ cm, ​then length $AE$ ​is

    1. (a)$1.5$ cm
    2. (b)$1$ cm
    3. (c)$2$ cm
    4. (d)$3$ cm
    Show answer

    (a) $1.5$ cm

    Step-by-step solution →
18. Q58 CBSE 2026
    $ABCD$ ​is a trapezium ​in which $AB\parallel DC$ and $E,F$ are points on $AD$ and $BC$ respectively ​such ​that $EF\parallel DC$. ​If $ED=36$ cm, $BF=70$ cm ​and $FC=30$ cm, then ​the length of $AD$ is :

    1. (a)$124$ cm
    2. (b)$120$ cm
    3. (c)$110$ cm
    4. (d)$114$ cm
    Show answer

    (b) $120$ cm

    Step-by-step solution →
19. Q59 CBSE 2026
    If $△ABC$ and $△DEF$ ​are ​similar such that $2AB=DE$ ​and $BC=8$ cm, ​then $EF$ is equal to ​:

    1. (a)$4$ cm
    2. (b)$8$ cm
    3. (c)$12$ cm
    4. (d)$16$ cm
    Show answer

    (d) $16$ cm

    Step-by-step solution →
20. Q60 CBSE 2026
    In ​the ​given figure, if $ME\parallel SU$, then ​which of ​the ​following ​statements ​is correct ​?

    1. (a)$△MOE\sim △SOU$
    2. (b)$△MOE\sim △SUO$
    3. (c)$△OEM\sim △USO$
    4. (d)$△OEM\sim △OSU$
    Show answer

    (d) $△OEM\sim △OSU$

    Step-by-step solution →