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 17 of 22

1. Q321 CBSE 2023
   Diagonals ​AC and ​BD of ​trapezium ABCD ​with $AB\parallel DC$ ​intersect each other at ​point O. Show that $\frac{OA}{OC}=\frac{OB}{OD}$.

   Show answer

   $△AOB\sim △COD$, hence $\frac{OA}{OC}=\frac{OB}{OD}$.

   Step-by-step solution →
2. Q322 CBSE 2023
   In ​the ​given ​figure, $\frac{BC}{BD}=\frac{BE}{AC}$ ​and $\angle ABD=\angle ACD$. Show ​that $△ABD\sim △EBC$.

   Show answer

   By SAS similarity, $△ABD\sim △EBC$.

   Step-by-step solution →
3. Q323 CBSE 2023
   In ​the given ​figure, $ABC$ ​and $AED$ ​are two right triangles, ​right angled ​at $B$ and $E$ ​respectively. Prove that:

   1. (i)$△ABC\sim △AED$
   2. (ii)$AB\times AD=AC\times AE$

   1. (i)Prove that triangle ABC ~ triangle AED.[2]
   2. (ii)Prove that AB x AD = AC x AE.[1]
   Show answer

   $△ABC\sim △AED$ (AA), hence $AB\times AD=AC\times AE$.

   Step-by-step solution →
4. Q324 CBSE 2023
   In ​the given ​figure, E ​is a point on the ​side CB produced of an ​isosceles triangle ABC with $AB=AC$. ​If $AD\perp BC$ and $EF\perp AC$, then ​prove that $△ABD\sim △ECF$.

   Show answer

   $△ABD\sim △ECF$ by the AA similarity criterion.

   Step-by-step solution →
5. Q325 CBSE 2023
   $ABCD$ is a trapezium ​in which $AB\parallel DC$ and ​its ​diagonals $AC$ ​and $BD$ intersect at $O$. ​Show ​that $\frac{OA}{OB}=\frac{OC}{OD}$.
   Show answer

   Proved: $\frac{OA}{OB}=\frac{OC}{OD}$

   Step-by-step solution →
6. Q326 CBSE 2023
   $E$ is ​a point ​on the ​side $AD$ produced of a ​parallelogram $ABCD$ and $BE$ intersects $CD$ ​at $F$. ​Show ​that $△ABE\sim △CFB$.

   Show answer

   $△ABE\sim △CFB$ by the AA criterion.

   Step-by-step solution →
7. Q327 CBSE 2023
   In the ​given figure, $CD$ ​is ​the ​perpendicular bisector of $AB$. $EF$ ​is perpendicular to $CD$. $AE$ ​intersects $CD$ at $G$. Prove ​that $\frac{CF}{CD}=\frac{FG}{DG}$.

   Show answer

   $\frac{CF}{CD}=\frac{FG}{DG}$ (proved)

   Step-by-step solution →
8. Q328 CBSE 2023
   In ​the ​given figure, $CM$ and $RN$ are respectively the medians of $△ABC$ ​and $△PQR$. ​If $△ABC\sim △PQR$, ​then prove ​that $△AMC\sim △PNR$.

   Show answer

   $△AMC\sim △PNR$ by the SAS similarity criterion.

   Step-by-step solution →
9. Q329 CBSE 2023
   In the given ​figure, $ABCD$ ​is ​a parallelogram. $BE$ bisects $CD$ ​at $M$ ​and intersects $AC$ ​at $L$. Prove that $EL=2BL$.

   Show answer

   $EL=2BL$ (proved)

   Step-by-step solution →
10. Q330 CBSE 2023
    $P$ ​and $Q$ are points on the ​sides $AB$ ​and $AC$ respectively of $△ABC$ such that $PQ\parallel BC$. ​If $AP=2$ cm, $PB=4$ cm and $PQ=3$ ​cm, ​then find the ​length ​of $BC$.
    Show answer

    $BC=9$ cm

    Step-by-step solution →
11. Q331 CBSE 2023
    Sides $AB$ ​and $BC$ ​and the ​median $AD$ of a triangle $ABC$ are respectively proportional to the ​sides $PQ$ and $QR$ ​and the median $PM$ of $△PQR$. ​Show ​that $△ABC\sim △PQR$.
    Show answer

    Proved: $△ABC\sim △PQR$

    Step-by-step solution →
12. Q332 CBSE 2023
    If AP ​and DQ are medians ​of triangles ​ABC and DEF respectively, ​where $△ABC\sim △DEF$, ​then ​prove that $\frac{AB}{DE}=\frac{AP}{DQ}$.
    Show answer

    $\frac{AB}{DE}=\frac{AP}{DQ}$ (proved).

    Step-by-step solution →
13. Q333 CBSE 2023
    Prove that ​each ​of ​the four triangles formed by ​joining the mid-points of the sides of a triangle ​are similar to the original triangle.
    Show answer

    All four sub-triangles are similar to $△ABC$ (ratio $1:2$).

    Step-by-step solution →
14. Q334 CBSE 2023
    A vertical ​pole ​of length $6$ m ​casts a shadow $4$ m long on the ground and at the same ​time a tower ​casts a ​shadow $28$ ​m long on the ground. Find the height ​of the tower.
    Show answer

    Height of tower $=42$ m

    Step-by-step solution →
15. Q335 CBSE 2023
    In ​the ​given figure, $DE\parallel AC$ ​and $DF\parallel AE$. ​Prove ​that $\frac{BF}{FE}=\frac{BE}{EC}$.

    Show answer

    $\frac{BF}{FE}=\frac{BE}{EC}$, proved.

    Step-by-step solution →
16. Q336 CBSE 2023
    The diagonals ​of a quadrilateral $ABCD$ ​intersect ​each other at ​the point $O$ such that $\frac{AO}{BO}=\frac{CO}{OD}$. ​Show that ​quadrilateral $ABCD$ is ​a ​trapezium.

    Show answer

    $AB\parallel DC$, so $ABCD$ is a trapezium.

    Step-by-step solution →
17. Q337 CBSE 2023
    If ​a ​line ​is drawn parallel ​to one side of a triangle to intersect the other two sides ​at distinct points, prove ​that the other two sides are ​divided in the same ratio.
    Show answer

    Hence $DE\parallel BC$ divides AB and AC in the same ratio: $\frac{AD}{DB}=\frac{AE}{EC}$.

    Step-by-step solution →
18. Q338 CBSE 2023
    If a line is drawn parallel ​to ​one ​side of a triangle to intersect the other two sides ​in distinct points, prove that the other two sides are divided in ​the same ratio.
    Show answer

    AD/DB = AE/EC. Hence proved (Basic Proportionality Theorem).

    Step-by-step solution →
19. Q339 CBSE 2023
    $D$ is a point on ​the ​side $BC$ ​of ​a triangle $ABC$ such ​that $\angle ADC=\angle BAC$, prove ​that $C{A}^2=CB\cdot CD$.
    Show answer

    $C{A}^2=CB\cdot CD$ (proved using AA similarity).

    Step-by-step solution →
20. Q340 CBSE 2023
    If a ​line is drawn ​parallel to one side of a ​triangle to intersect the other ​two ​sides at ​distinct points, then prove that the other two sides ​are divided in the same ratio.
    Show answer

    $\frac{AD}{DB}=\frac{AE}{EC}$, proving the Basic Proportionality Theorem.

    Step-by-step solution →