Chapter 6 · Triangles

NCERT Exemplar Class 10 Maths Exercise 6.1

All 12 questions of NCERT Exemplar Class 10 Maths Exercise 6.1 (Triangles), in the book's order, each with its answer and a step-by-step solution.

1. Q1
   In ​Fig. ​6.2, $\angle BAC=90^{\circ }$ ​and $AD\perp BC$. Then,

   1. (a)$BD\cdot CD=B{C}^2$
   2. (b)$AB\cdot AC=B{C}^2$
   3. (c)$BD\cdot CD=A{D}^2$
   4. (d)$AB\cdot AC=A{D}^2$
   Show answer

   (c) $BD\cdot CD=A{D}^2$

   Step-by-step solution →
2. Q2
   The lengths ​of the diagonals of a ​rhombus ​are 16 cm ​and 12 ​cm. Then, the length ​of the side of the rhombus ​is

   1. (a)$9$ cm
   2. (b)$10$ cm
   3. (c)$8$ cm
   4. (d)$20$ cm
   Show answer

   (b) $10$ cm

   Step-by-step solution →
3. Q3
   If $△ABC\sim △EDF$ and $△ABC$ ​is ​not ​similar to $△DEF$, then which ​of the following is not true?

   1. (a)$BC\cdot EF=AC\cdot FD$
   2. (b)$AB\cdot EF=AC\cdot DE$
   3. (c)$BC\cdot DE=AB\cdot EF$
   4. (d)$BC\cdot DE=AB\cdot FD$
   Show answer

   (c) $BC\cdot DE=AB\cdot EF$

   Step-by-step solution →
4. Q4
   If ​in ​two triangles ABC and PQR, $\frac{AB}{QR}=\frac{BC}{PR}=\frac{CA}{PQ}$, ​then

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

   (a) $△PQR\sim △CAB$

   Step-by-step solution →
5. Q5
   In Fig. 6.3, two line ​segments $AC$ ​and $BD$ ​intersect ​each other at the point $P$ such ​that $PA=6$ cm, $PB=3$ cm, $PC=2.5$ cm, $PD=5$ cm, $\angle APB=50^{\circ }$ and $\angle CDP=30^{\circ }$. Then, $\angle PBA$ is ​equal ​to

   1. (a)$50^{\circ }$
   2. (b)$30^{\circ }$
   3. (c)$60^{\circ }$
   4. (d)$100^{\circ }$
   Show answer

   (d) $100^{\circ }$

   Step-by-step solution →
6. Q6
   If in ​two ​triangles DEF and PQR, $\angle D=\angle Q$ ​and $\angle R=\angle E$, then ​which of the ​following ​is not ​true?

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

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

   Step-by-step solution →
7. Q7
   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)similar but not congruent
   3. (c)neither congruent nor similar
   4. (d)congruent as well as similar
   Show answer

   (b) similar but not congruent

   Step-by-step solution →
8. Q8
   It ​is given that $△ABC\sim △PQR$, with $\frac{BC}{QR}=\frac{1}{3}$. ​Then, $\frac{\mathrm{ar}(PRQ)}{\mathrm{ar}(BCA)}$ ​is ​equal ​to

   1. (a)$9$
   2. (b)$3$
   3. (c)$\frac{1}{3}$
   4. (d)$\frac{1}{9}$
   Show answer

   (a) $9$

   Step-by-step solution →
9. Q9
   It is ​given ​that $△ABC\sim △DFE$, $\angle A=30^{\circ }$, $\angle C=50^{\circ }$, $AB=5$ cm, $AC=8$ ​cm ​and $DF=7.5$ cm. ​Then, ​the ​following ​is true:

   1. (a)$DE=12$ cm, $\angle F=50^{\circ }$
   2. (b)$DE=12$ cm, $\angle F=100^{\circ }$
   3. (c)$EF=12$ cm, $\angle D=100^{\circ }$
   4. (d)$EF=12$ cm, $\angle D=30^{\circ }$
   Show answer

   (b) $DE=12$ cm, $\angle F=100^{\circ }$

   Step-by-step solution →
10. Q10
    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. Q11
    If $△ABC\sim △QRP$, $\frac{\text{ar}(ABC)}{\text{ar}(PQR)}=\frac{9}{4}$, $AB=18$ ​cm ​and $BC=15$ cm, ​then ​PR is ​equal ​to

    1. (a)$10$ cm
    2. (b)$12$ cm
    3. (c)$\frac{20}{3}$ cm
    4. (d)$8$ cm
    Show answer

    (a) $10$ cm

    Step-by-step solution →
12. Q12
    If ​S ​is ​a point on side PQ ​of a $△PQR$ such ​that $PS=QS=RS$, ​then

    1. (a)$PR\cdot QR=R{S}^2$
    2. (b)$Q{S}^2+R{S}^2=Q{R}^2$
    3. (c)$P{R}^2+Q{R}^2=P{Q}^2$
    4. (d)$P{S}^2+R{S}^2=P{R}^2$
    Show answer

    (c) $P{R}^2+Q{R}^2=P{Q}^2$

    Step-by-step solution →