Triangles: 1 mark Questions (CBSE Class 10)

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

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.

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

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

Shown below are three triangles. The measures of two adjacent sides and included angle are given for each triangle :
Which of these triangles are similar ?

1. (A)$△RPQ$ and $△XZY$
2. (B)$△RPQ$ and $△MNL$
3. (C)$△XZY$ and $△MNL$
4. (D)$△RPQ$, $△XZY$ and $△MNL$ are similar to one another

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

In the given figure $△ABC$ is shown, in which DE $\parallel$ BC. If AD = 5 cm, DB = 2.5 cm and DE = 8 cm, then the length of BC is :

1. (A)10 cm
2. (B)6 cm
3. (C)12 cm
4. (D)7.5 cm

In $\Delta$ DEF, AB $\parallel$ EF. The value of $x$ is :

1. (A)0, 2
2. (B)2 only
3. (C)– 2
4. (D)1

It is given that $\Delta$ ABC ~ $\Delta$ 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

In the given figure, OA $\times$ OB = OC $\times$ OD. Which of the following option is correct ?

1. (A)$\angle A=\angle C$
2. (B)$\angle A=\angle B$
3. (C)$\angle A=\angle D$
4. (D)$\Delta OAD\sim \Delta OBC$

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)$\frac{AB+BC}{AC}=\frac{DE+DF}{EF}$

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

ABCD is a parallelogram such that AF = 7 cm, FB = 3 cm and EF = 4 cm, length FD = equals

1. (A)$\frac{21}{4}$ cm
2. (B)$\frac{28}{3}$ cm
3. (C)$\frac{12}{7}$ cm
4. (D)5.5 cm

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

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

In the given figure, $AB\parallel EF$. If AB = 24 cm, EF = 36 cm and DA = 7 cm, then AE equals

1. (A)2.5 cm
2. (B)10.5 cm
3. (C)3.5 cm
4. (D)$\frac{14}{3}$ cm

Which of the following is not the criterion for similarity of triangles ?

1. (A)AAA
2. (B)SSS
3. (C)SAS
4. (D)RHS

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

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

Assertion (A) : All congruent triangles are similar.
Reason (R) : In congruent triangles, the ratio of corresponding sides is 1 : 1.

1. (A)Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
2. (B)Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).
3. (C)Assertion (A) is true, but Reason (R) is false.
4. (D)Assertion (A) is false, but Reason (R) is true.

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

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)$x=12$, $y=3.2$

In $△$ ABC, PQ $\parallel$ BC. It is given that AP = 2.4 cm, PB = 3.6 cm and BC = 5.4 cm. PQ is equal to :

1. (A)2.7 cm
2. (B)1.8 cm
3. (C)3.6 cm
4. (D)2.16 cm

In $△ABC$, DE $\parallel$ BC. If AE = $(2x+1)$ cm, EC = 4 cm, AD = $(x+1)$ cm and DB = 3 cm, then value of $x$ is

1. (A)1
2. (B)$\frac{1}{2}$
3. (C)$-1$
4. (D)$\frac{1}{3}$

Assertion (A) : $△ABC\sim △PQR$ such that $\angle A=65^{\circ }$, $\angle C=60^{\circ }$. Hence $\angle Q=55^{\circ }$.
Reason (R) : Sum of all angles of a triangle is $180^{\circ }$.

1. (A)Both Assertion (A) and Reason (R) are true and Reason (R) is correct explanation of Assertion (A).
2. (B)Both Assertion (A) and Reason (R) are true, but Reason (R) is not correct explanation for Assertion (A).
3. (C)Assertion (A) is true, but Reason (R) is false.
4. (D)Assertion (A) is false, but Reason (R) is true.

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

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

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.

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)$\frac{DE}{QR}=\frac{DF}{PQ}$
2. (B)$\frac{EF}{PR}=\frac{DF}{PQ}$
3. (C)$\frac{EF}{RP}=\frac{DE}{QR}$
4. (D)$\frac{DE}{PQ}=\frac{EF}{RP}$

The measurements of $△LMN$ and $△ABC$ are shown in the figure given below. The length of side AC is :

1. (A)16 cm
2. (B)7 cm
3. (C)8 cm
4. (D)4 cm

In the given figure, in $△ABC$, $AD\perp BC$ and $\angle BAC=90^{\circ }$. If BC = 16 cm and DC = 4 cm, then the value of $x$ is :

1. (A)4 cm
2. (B)5 cm
3. (C)8 cm
4. (D)3 cm

$△ABC$ 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)$40^{\circ }$

E and F are points on the sides AB and AC respectively of a $△ABC$ such that $\frac{AE}{EB}=\frac{AF}{FC}=\frac{1}{2}$. Which of the following relation is true ?

1. (A)$EF=2BC$
2. (B)$BC=2EF$
3. (C)$EF=3BC$
4. (D)$BC=3EF$

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.

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

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

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)$180^{\circ }$

Assertion (A) : A line drawn parallel to any one side of a triangle intersects the other two sides in the same ratio.
Reason (R) : Parallel lines cannot be drawn to any side of a triangle.

1. (A)Both Assertion (A) and Reason (R) are correct and Reason (R) is the correct explanation of Assertion (A).
2. (B)Both Assertion (A) and Reason (R) are correct but Reason (R) is not the correct explanation of Assertion (A).
3. (C)Assertion (A) is true, but Reason (R) is false.
4. (D)Assertion (A) is false, but Reason (R) is true.

If in the given figure, $DE\parallel BC$. If $AD=2.8$ cm, $DB=2.1$ cm and $EC=4.8$ cm, then the value of $x$ is :

1. (A)3.6 cm
2. (B)2.4 cm
3. (C)6.4 cm
4. (D)4.8 cm

In the given figure, if $△ABC\sim △QPR$, then the value of $x$ is :

1. (A)$5.3$ cm
2. (B)$4.6$ cm
3. (C)$2.3$ cm
4. (D)4 cm

It is given that $△ABC\sim △DEF$. If $\angle A=55^{\circ }$, $\angle E=45^{\circ }$, then $\angle C$ is :

1. (A)$80^{\circ }$
2. (B)$90^{\circ }$
3. (C)$55^{\circ }$
4. (D)$45^{\circ }$

In the given figure, in $△ABC$, DE $\parallel$ BC. If AD = 2x cm, AE = (x + 2) cm, DB = 4 cm, EC = 3 cm, then the value of x is :

1. (A)3
2. (B)2
3. (C)6
4. (D)4

In the given figure $△ABC$ is shown. DE is parallel to BC. If AD = 5 cm, DB = 2.5 cm and BC = 12 cm, then DE is equal to

1. (A)10 cm
2. (B)6 cm
3. (C)8 cm
4. (D)7.5 cm

The perimeters of two similar triangles ABC and PQR are 56 cm and 48 cm respectively. PQ/AB is equal to

1. (A)$\frac{7}{8}$
2. (B)$\frac{6}{7}$
3. (C)$\frac{7}{6}$
4. (D)$\frac{8}{7}$

AB and CD are two chords of a circle intersecting at P. Choose the correct statement from the following :

1. (A)$△ADP\sim △CBA$
2. (B)$△ADP\sim △BPC$
3. (C)$△ADP\sim △BCP$
4. (D)$△ADP\sim △CBP$

If the diagonals of a quadrilateral divide each other proportionally, then it is a :

1. (A)parallelogram
2. (B)rectangle
3. (C)square
4. (D)trapezium

In $△ABC$, DE $\parallel$ BC (as shown in the figure). If AD = 2 cm, BD = 3 cm, BC = 7.5 cm, then the length of DE (in cm) is :

1. (A)2.5
2. (B)3
3. (C)5
4. (D)6

In $△ABC$, DE $\parallel$ BC (as shown in the figure). If AD = 4 cm, AB = 9 cm and AC = 13.5 cm, then the length of EC is :

1. (A)6 cm
2. (B)7.5 cm
3. (C)9 cm
4. (D)5.7 cm

In the given figure, in $△ABC$, DE $\parallel$ BC. If AD = 2.4 cm, DB = 4 cm and AE = 2 cm, then the length of AC is :

1. (A)$\frac{10}{3}$ cm
2. (B)$\frac{3}{10}$ cm
3. (C)$\frac{16}{3}$ cm
4. (D)1.2 cm

If a vertical pole of length 7.5 m casts a shadow 5 m long on the ground and at the same time, a tower casts a shadow 24 m long, then the height of the tower is :

1. (A)20 m
2. (B)40 m
3. (C)60 m
4. (D)36 m

Assertion (A) : ABCD is a trapezium with DC $\parallel$ AB. E and F are points on AD and BC respectively, such that EF $\parallel$ AB. Then $\frac{AE}{ED}=\frac{BF}{FC}$.
Reason (R) : Any line parallel to parallel sides of a trapezium divides the non-parallel sides proportionally.

1. (A)Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
2. (B)Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).
3. (C)Assertion (A) is true, but Reason (R) is false.
4. (D)Assertion (A) is false, but Reason (R) is true.

The sides of two similar triangles are in the ratio 4 : 7. The ratio of their perimeters is

1. (A)4 : 7
2. (B)12 : 21
3. (C)16 : 49
4. (D)7 : 4

In the given figure, AB $\parallel$ CD. If AB = 5 cm, CD = 2 cm and OB = 3 cm, then the length of OC is

1. (A)$\frac{15}{2}$ cm
2. (B)$\frac{10}{3}$ cm
3. (C)$\frac{6}{5}$ cm
4. (D)$\frac{3}{5}$ cm

In the above figure, the criterion of similarity by which $△ABC\sim △PQR$ is :

1. (A)SSA (Side – Side – Angle) Similarity
2. (B)ASA (Angle – Side – Angle) Similarity
3. (C)SAS (Side – Angle – Side) Similarity
4. (D)AA (Angle – Angle) Similarity

If $△ABC\sim △DEF$ and $\angle A=47^{\circ }$, $\angle E=83^{\circ }$, then $\angle C$ is equal :

1. (A)$47^{\circ }$
2. (B)$50^{\circ }$
3. (C)$83^{\circ }$
4. (D)$130^{\circ }$

$△ABC\sim △DEF$ and their perimeters are 32 cm and 24 cm respectively. If AB = 10 cm, then DE equals :

1. (A)8 cm
2. (B)7.5 cm
3. (C)15 cm
4. (D)$5\sqrt{3}$ cm

In the given figure, AD = 2 cm, DB = 3 cm, DE = 2.5 cm and DE $\parallel$ BC. The value of x is :

1. (A)6 cm
2. (B)3.75 cm
3. (C)6.25 cm
4. (D)7.5 cm

In two triangles $△PQR$ and $△ABC$, it is given that $\frac{AB}{BC}=\frac{PQ}{PR}$. For these two triangles to be similar, which of the following should be true ?

1. (A)$\angle A=\angle P$
2. (B)$\angle B=\angle Q$
3. (C)$\angle B=\angle P$
4. (D)CA = QR

In the given figure, ABC is a triangle in which AD = 1.6 cm, BD = 4.8 cm, AE = 1.1 cm and EC = 2.2 cm. Then :

1. (A)DE $\parallel$ BC
2. (B)DE = $\frac{1}{2}$BC
3. (C)DE = BC
4. (D)DE is not parallel to BC (DE $\nparallel$ BC)

If $△ABC\sim △PQR$ with $\angle A=32^{\circ }$ and $\angle R=65^{\circ }$, then the measure of $\angle B$ is :

1. (A)$32^{\circ }$
2. (B)$65^{\circ }$
3. (C)$83^{\circ }$
4. (D)$97^{\circ }$

In the given figure, $DE\parallel BC$. If AD = 2 units, DB = AE = 3 units and EC = x units, then the value of x is :

1. (A)2
2. (B)3
3. (C)5
4. (D)$\frac{9}{2}$

In the given figure, $AB\parallel PQ$. If AB = 6 cm, PQ = 2 cm and OB = 3 cm, then the length of OP is :

1. (A)9 cm
2. (B)3 cm
3. (C)4 cm
4. (D)1 cm

In the given figure, $\angle A=\angle C$, AB = 6 cm, AP = 12 cm, CP = 4 cm. Then length of CD is :

1. (A)2 cm
2. (B)6 cm
3. (C)8 cm
4. (D)18 cm

In the given figure, $△ABC\sim △QPR$. If AC = 6 cm, BC = 5 cm, QR = 3 cm and PR = x; then the value of x is :

1. (A)3.6 cm
2. (B)2.5 cm
3. (C)10 cm
4. (D)3.2 cm

In $△ABC$, PQ $\parallel$ BC. If PB = 6 cm, AP = 4 cm, AQ = 8 cm, find the length of AC.

1. (A)12 cm
2. (B)20 cm
3. (C)6 cm
4. (D)14 cm

In the given figure, PQ $\parallel$ AC. If BP = 4 cm, AP = 2.4 cm and BQ = 5 cm, then length of BC is :

1. (A)8 cm
2. (B)3 cm
3. (C)0.3 cm
4. (D)$\frac{25}{3}$ cm

In the given figure, DE $\parallel$ BC. The value of x is :

1. (A)6
2. (B)12.5
3. (C)8
4. (D)10

In $△ABC$ and $△DEF$, $\frac{AB}{DE}=\frac{BC}{FD}$. Which of the following makes the two triangles similar ?

1. (A)$\angle A=\angle D$
2. (B)$\angle B=\angle D$
3. (C)$\angle B=\angle E$
4. (D)$\angle A=\angle F$

If $△PQR\sim △ABC$; PQ = 6 cm, AB = 8 cm and the perimeter of $△ABC$ is 36 cm, then the perimeter of $△PQR$ is

1. (A)20.25 cm
2. (B)27 cm
3. (C)48 cm
4. (D)64 cm

In the given figure, DE$\parallel$BC. If AD = 3 cm, AB = 7 cm and EC = 3 cm, then the length of AE is

1. (A)2 cm
2. (B)2.25 cm
3. (C)3.5 cm
4. (D)4 cm