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 8 of 22

1. Q141 CBSE 2025
   In the ​given ​figure, in $△PQR$, $ST\parallel QR$. If $PS=16$ ​mm and $PQ=40$ ​mm, then $PT:TR$ ​is ​:

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

   (a) $2:3$

   Step-by-step solution →
2. Q142 CBSE 2025
   Which ​of ​the following is ​an ​**incorrect** statement?

   1. (a)Two congruent triangles are also similar.
   2. (b)A square and a rhombus are not similar.
   3. (c)Two triangles are similar if their corresponding sides are proportional.
   4. (d)Two polygons are similar if and only if their corresponding sides are in proportion.
   Show answer

   (d) Two polygons are similar if and only if their corresponding sides are in proportion.

   Step-by-step solution →
3. Q143 CBSE 2025
   If $△ABC\sim △DEF$ ​such that $3AB=2DE$ and $BC=8$ ​cm, ​then $EF$ is ​equal to:

   1. (a)$\frac{16}{3}$ cm
   2. (b)$12$ cm
   3. (c)$\frac{4}{3}$ cm
   4. (d)$48$ cm
   Show answer

   (b) $12$ cm

   Step-by-step solution →
4. Q144 CBSE 2025
   In ​the adjoining ​figure, $PQ\parallel XY\parallel BC$, $AP=2$ cm, $PX=1.5$ ​cm ​and $BX=4$ ​cm. ​If $QY=0.75$ ​cm, then $AQ+CY=$

   1. (a)$6$ cm
   2. (b)$4.5$ cm
   3. (c)$3$ cm
   4. (d)$5.25$ cm
   Show answer

   (c) $3$ cm

   Step-by-step solution →
5. Q145 CBSE 2025
   Which ​of the following ​is not the ​criterion for ​similarity ​of triangles?

   1. (a)AAA
   2. (b)SSS
   3. (c)SAS
   4. (d)RHS
   Show answer

   (d) RHS

   Step-by-step solution →
6. Q146 CBSE 2025
   Given $△ABC\sim △PQR$, $\angle A=30^{\circ }$ ​and $\angle Q=90^{\circ }$. The ​value ​of $(\angle R+\angle B)$ ​is

   1. (a)$90^{\circ }$
   2. (b)$120^{\circ }$
   3. (c)$150^{\circ }$
   4. (d)$180^{\circ }$
   Show answer

   (c) $150^{\circ }$

   Step-by-step solution →
7. Q147 CBSE 2025
   In a $△ABC$, $DE$ ​is ​drawn parallel ​to $BC$ ​with $D$ being on side $AB$ ​and $E$ ​being on side $AC$. If $AD=x$, $DB=3x+4$, $AE=x+3$ and $AC=4x+22$, ​then ​value of $x$ is:

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

   (c) $2$

   Step-by-step solution →
8. Q148 CBSE 2025
   $△ABC$ and $△PQR$ ​are ​shown in the ​adjoining figures. ​The ​measure ​of $\angle C$ ​is:

   1. (a)$140^{\circ }$
   2. (b)$80^{\circ }$
   3. (c)$60^{\circ }$
   4. (d)$40^{\circ }$
   Show answer

   (d) $40^{\circ }$

   Step-by-step solution →
9. Q149 CBSE 2025
   In ​the ​given figure, $PQ\parallel BC$. If $\frac{AP}{PB}=\frac{4}{13}$ and $AC=20.4$ cm, then ​the ​length ​of $AQ$ is ​:

   1. (a)$2.8$ cm
   2. (b)$5.8$ cm
   3. (c)$3.8$ cm
   4. (d)$4.8$ cm
   Show answer

   (d) $4.8$ cm

   Step-by-step solution →
10. Q150 CBSE 2025
    If ​in ​triangles $ABC$ ​and $DEF$, $\frac{AB}{DE}=\frac{BC}{FD}$, then ​they ​will ​be similar, when:

    1. (a)$\angle B=\angle E$
    2. (b)$\angle A=\angle D$
    3. (c)$\angle B=\angle D$
    4. (d)$\angle A=\angle F$
    Show answer

    (c) $\angle B=\angle D$

    Step-by-step solution →
11. Q151 CBSE 2025
    In ​the ​given figure, ​if $DE\parallel BC$, $AD=1.5$ cm, $DB=3$ cm and $EC=2$ cm, ​the ​length of $AC$ ​is ​:

    1. (a)1.5 cm
    2. (b)3 cm
    3. (c)3.5 cm
    4. (d)4.5 cm
    Show answer

    (b) 3 cm

    Step-by-step solution →
12. Q152 CBSE 2025
    In ​triangles ​ABC and ​DEF, $\angle B=\angle E$, $\angle F=\angle C$ and $AB=3DE$. Then, ​the ​two ​triangles ​are :

    1. (a)congruent but not similar
    2. (b)congruent as well as similar
    3. (c)neither congruent nor similar
    4. (d)similar but not congruent
    Show answer

    (d) similar but not congruent

    Step-by-step solution →
13. Q153 CBSE 2025
    Which of ​the ​following statements ​is false?

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

    (a) Two right triangles are always similar.

    Step-by-step solution →
14. Q154 CBSE 2025
    From ​the figures given ​below, which ​of ​the ​following ​is true about the ​measure of $\angle P$?

    1. (a)$\angle P=60^{\circ }$
    2. (b)$\angle P=80^{\circ }$
    3. (c)$\angle P=40^{\circ }$
    4. (d)The measure of $\angle P$ cannot be determined
    Show answer

    (c) $\angle P=40^{\circ }$

    Step-by-step solution →
15. Q155 CBSE 2025
    Which ​of the ​following ​statements is ​**incorrect**?

    1. (a)Two congruent figures are always similar.
    2. (b)A square and a rhombus of the same area are always similar.
    3. (c)Two equilateral triangles are always similar.
    4. (d)Two similar triangles need not be congruent.
    Show answer

    (b) A square and a rhombus of the same area are always similar.

    Step-by-step solution →
16. Q156 CBSE 2025
    In ​the ​adjoining ​figure, $ABCD$ ​is a ​trapezium in which $XY\parallel AB\parallel CD$. If $AX=\frac{2}{3}AD$, ​then $CY:YB=$

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

    (d) $1:2$

    Step-by-step solution →
17. Q157 CBSE 2025
    Which ​types ​of triangles ​are ​always ​similar?

    1. (a)Right-angled triangles
    2. (b)Acute-angled triangles
    3. (c)Isosceles triangles
    4. (d)Equilateral triangles
    Show answer

    (d) Equilateral triangles

    Step-by-step solution →
18. Q158 CBSE 2025
    If in ​two triangles $△DEF$ and $△PQR$, $\angle D=\angle Q$ and $\angle R=\angle E$, then which of ​the ​following ​is $\text{not}$ ​true ​?

    1. (a)$\frac{DE}{QR}=\frac{DF}{PQ}$
    2. (b)$\frac{EF}{PR}=\frac{DF}{PQ}$
    3. (c)$\frac{EF}{RP}=\frac{DE}{QR}$
    4. (d)$\frac{DE}{PQ}=\frac{EF}{RP}$
    Show answer

    (d) $\frac{DE}{PQ}=\frac{EF}{RP}$

    Step-by-step solution →
19. Q159 CBSE 2025
    What ​values ​of $x$ and $y$ ​will make $△ABC$ similar ​to $△QRP$ ​in the figures ​given below?

    1. (a)$x=6,y=5$
    2. (b)$x=5,y=6$
    3. (c)$x=6,y=6$
    4. (d)$x=4.8,y=3.2$
    Show answer

    (b) $x=5,y=6$

    Step-by-step solution →
20. Q160 CBSE 2025
    If $△ABC\sim △PQR$ such ​that $AB=6$ ​cm, $AC=7$ cm, $QR=15$ ​cm and $PQ=12$ ​cm, then ​the sum of lengths of $BC$ and $PR$ is

    1. (a)$44$ cm
    2. (b)$21.5$ cm
    3. (c)$21$ cm
    4. (d)$29.5$ cm
    Show answer

    (b) $21.5$ cm

    Step-by-step solution →