Class 10 Practice – Level 1 – Triangles

Total questions: 40

The corresponding sides of two similar triangles are in the ratio 3 : 4, then the ratios of the area of triangles is:

Topic: Areas of Similar Triangles

$ \displaystyle \frac{9}{{16}}$

$ \displaystyle \frac{8}{{14}}$

$ \displaystyle \frac{4}{{10}}$

$ \displaystyle \frac{6}{{12}}$

None

Two triangles are similar if their corresponding sides are _________.

Topic: Criteria for Similarity of Triangles

Opposite

Equal

Proportional

None of these

None

In the given figure , ABC is an isosceles triangle right angled at C with AC = 4 cm. What is the length of AB?

Topic: Isosceles Right Triangle Properties

$ \displaystyle 12\sqrt{6}cm$

$ \displaystyle 14\sqrt{5}cm$

$ \displaystyle 6\sqrt{3}cm$

$ \displaystyle 4\sqrt{2}cm$

None

Given △ABC ∼ △PQR, if $ \displaystyle \dfrac{{\text{AB}}}{{\text{PQ}}}=\dfrac{1}{3},$ then find $ \displaystyle \dfrac{{\text{ar}\Delta \text{ABC}}}{{\text{ar}\Delta \text{PQR}}}$:

Topic: Areas of Similar Triangles

$ \displaystyle \dfrac{8}{16}$

$ \displaystyle \dfrac{1}{9}$

$ \displaystyle \dfrac{2}{8}$

$ \displaystyle \dfrac{3}{6}$

None

The perimeters of two similar triangles are 25 cm and 15 cm respectively. If one side of the first triangle is 9 cm, find the corresponding side of the second triangle.

Topic: Criteria for Similarity of Triangles

5.4 cm

4.2 cm

3 cm

6.5 cm

None

If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points then:

Topic: Basic Proportionality Theorem

The other two sides are divided in the different ratio

The other two sides are divided in the same ratio

The other two sides are not divided in any ratio

None of the above

None

The ratio of the areas of two similar triangles is:

Topic: Areas of Similar Triangles

Equal to the ratio of the cubes of their corresponding sides.

Not equal to the ratio of the squares of their corresponding sides.

Equal to the ratio of the squares of their corresponding sides.

None

In △ABC, if DE ∥ BC, then which of the following statements is true?

Topic: Basic Proportionality Theorem

$ \displaystyle \dfrac{{AD}}{{DB}}=\dfrac{{AE}}{{EC}}$

$ \displaystyle \dfrac{{AD}}{{DB}}=\dfrac{{AC}}{{EC}}$

$ \displaystyle \dfrac{{AD}}{{AB}}=\dfrac{{AE}}{{AC}}$

All of the above

None

If in two triangles DEF and PQR, ∠D = ∠Q and ∠R = ∠E, then which of the following is not true?

Topic: Criteria for Similarity of Triangles

$ \displaystyle \dfrac{{EF}}{{PR}}=\dfrac{{DF}}{{PQ}}$

$ \displaystyle \dfrac{{DE}}{{PQ}}=\dfrac{{EF}}{{RP}}$

$ \displaystyle \dfrac{{DE}}{{QR}}=\dfrac{{DF}}{{PQ}}$

$ \displaystyle \dfrac{{EF}}{{RP}}=\dfrac{{DE}}{{QR}}$

None

10.

It is given that △ABC ∼ △PQR, with $ \displaystyle \dfrac{{\text{BC}}}{{\text{QR}}}=\dfrac{1}{3}.$ Then, $ \displaystyle \dfrac{{\text{ar}\Delta \text{PRQ}}}{{\text{ar}\Delta \text{BCA}}}$ is equal to:

Topic: Areas of Similar Triangles

$ \displaystyle \dfrac{1}{3}$

$ \displaystyle \dfrac{1}{9}$

None

11.

If in triangles ABC and DEF, $ \displaystyle \dfrac{{\text{AD}}}{{\text{DE}}}=\dfrac{{\text{BC}}}{{\text{FD}}},$ then they will be similar, when

Topic: Criteria for Similarity of Triangles

∠B = ∠E

∠A = ∠D

∠B = ∠D

∠A = ∠F

None

12.

The perimeters of two similar triangles are 25 cm and 15 cm respectively. If one side of the first triangle is 9 cm, then the corresponding side of second triangle is:

Topic: Ratios of Corresponding Sides of Similar Triangles

2.3

5.4

6.2

7.9

None

13.

In ΔABC, DE || BC such that AD = 2.4 cm, AB = 3.2 cm and AC = 8 cm, then what is the length of AE?

Topic: Basic Proportionality Theorem

Similarity of triangle and its criterias

8 cm

10 cm

4 cm

6 cm

None

14.

In the given figure, D and E are points on sides AB and AC respectively of a △ABC such that DE∣∣BC. If AD = 3.6 cm, AB = 10 cm and AE = 4.5 cm, find EC.

Topic: Basic Proportionality Theorem

10 cm

12 cm

8 cm

6 cm

None

15.

If △ABC ∼ △DEF such that AB = 1.2 cm and DE = 1.4 cm, the ratio of the areas of △ABC and △DEF is:

Topic: Areas of Similar Triangles

49 : 36

6 : 7

7 : 6

36 : 49

None

16.

The triangle whose vertices are (2, 4), (5,1) and (6, 5) will be:

Topic: Properties of Triangles

Isosceles triangle

Equilateral triangle

Scalene triangle

None of the above

None

17.

ABC is an isosceles triangle, right angled at C. Then, $ \displaystyle {\text{A}{{\text{B}}^{2}}}$ will be equal to:

Topic: Pythagoras Theorem in Triangles

2 $ \displaystyle {\text{A}{{\text{C}}^{2}}}$

$ \displaystyle {\text{A}{{\text{C}}^{2}}}$

$ \displaystyle {\text{B}{{\text{C}}^{2}}}$

2 $ \displaystyle {\text{B}{{\text{C}}^{2}}}$

None

18.

The area of two similar triangles ABC and PQR are in the ratio 9 : 16. If BC = 4.5cm, find the length of QR.

Topic: Areas of Similar Triangles

12 cm

6 cm

8 cm

10 cm

None

19.

The corresponding altitudes of two similar triangles are 6cm and 9cm respectively. Find the ratio of their areas.

Topic: Areas of Similar Triangles

$ \displaystyle \dfrac{4}{9}$

$ \displaystyle \dfrac{6}{12}$

$ \displaystyle \dfrac{2}{8}$

$ \displaystyle \dfrac{5}{8}$

None

20.

A ladder 10 m long reaches a window 8 m above the ground. Find the distance of the foot of the ladder from the base of the wall.

Topic: Application of Pythagoras Theorem

8 m

4 m

2 m

6 m

None

21.

If a line intersects sides AB and AC of a △ABC at D and E respectively and is parallel to BC. Then, $ \displaystyle \dfrac{{\text{AD}}}{{\text{AB}}}\,\text{ }$ will be equal to:

Topic: Criteria for Similarity of Triangles

$ \displaystyle \dfrac{{\text{AB}}}{{\text{AC}}}\,\text{ }$

$ \displaystyle \dfrac{{\text{AE}}}{{\text{AC}}}\,\text{ }$

$ \displaystyle \dfrac{{\text{AE}}}{{\text{AD}}}\,\text{ }$

$ \displaystyle \dfrac{{\text{BC}}}{{\text{AC}}}\,\text{ }$

None

22.

In the given figure, if PQ ∥ RS, then is it true that ΔPOQ ∼ ΔSOR?

Topic: Right-Angled Triangles

True

False

Cannot be determined

Incomplete information

None

23.

A ladder is placed against a wall such that its foot is at a distance of 2.5 m from the wall and its top reaches a window 6 m above the ground. Find the length of the ladder.

Topic: Pythagoras Theorem in Triangles

5.5 m

4 m

6.5 m

2.8 m

None

24.

In the given figure, if AD ⊥ BC, then, $ \displaystyle \text{A}{{\text{B}}^{2}}+\text{C}{{\text{D}}^{2}}$ will be equal to:

Topic: Application of Pythagoras Theorem

$ \displaystyle\text{B}{{\text{D}}^{2}}+\text{A}{{\text{C}}^{2}}$

$ \displaystyle\text{A}{{\text{D}}^{2}}+\text{A}{{\text{B}}^{2}}$

$ \displaystyle\text{A}{{\text{D}}^{2}}+\text{A}{{\text{C}}^{2}}$

$ \displaystyle\text{B}{{\text{D}}^{2}}+\text{A}{{\text{D}}^{2}}$

None

25.

State whether the given quadrilaterals are similar or not:

Topic: Criteria for Similarity of Triangles

(i)

(ii)

Similar

Not similar

Incomplete information

Cannot be predicted

None

26.

In the given figures, DE ∣∣ BC. Find EC in (i) and AD in (ii) respectively.

Topic: Basic Proportionality Theorem

6.5 cm, 3.4 cm

3.2 cm, 2.0 cm

2.4 cm, 5.4 cm

2.0 cm, 2.4 cm

None

27.

The figure of two triangles are given below. Based on these triangles, select the correct option.

Topic: Criteria for Congruence

∠J≅∠V

∠B≅∠D

XJ≅∠V

∠H≅∠I

None

28.

Which of the following is not a criterion for congruence of triangles?

Topic: Criteria for Congruence

SAS

SSS

ASA

SSA

None

29.

A triangle ABC is right-angled at B. Given that AB=9 cm, AC=15 cm, calculate the length of BC?

Topic: Pythagoras Theorem

15 cm

18 cm

12 cm

21 cm

None

30.

If △ABC≅△LKM, Which side of △LKM is equal to side AC of △ABC?

Topic: Criteria for Congruence

All of the above

None

31.

In the given figure, if AB=AC and BD=DC⋅ △ABD and △ACD are congruent by which criterion?

Topic: Criteria for Congruence

SSS

ASA

SAS

RHS

None

32.

For given figure, which one is correct:

Topic: Application of Pythagoras Theorem

△ABC≅△DEF

△ABC≅△FED

△ABC≅EDF

△ABC≅△DFE

None

33.

In an obtuse △ABC ( ∠B is obtuse), AD is perpendicular to CB produced. Then, $ \displaystyle \text{A}{{\text{B}}^{2}}+\text{B}{{\text{C}}^{2}}+2\text{BC}\times \text{BD}$ will be equal to:

Topic: Pythagoras Theorem in Triangles

$ \displaystyle {\text{A}{{\text{D}}^{2}}}$

$ \displaystyle {\text{A}{{\text{C}}^{2}}}$

$ \displaystyle {\text{D}{{\text{C}}^{2}}}$

$ \displaystyle {\text{D}{{\text{B}}^{2}}}$

None

34.

In the given figure, DE∥BC, AD = 1 cm and BD = 2 cm. What is the ratio of the ar(△ABC) to the ar ( △ADE) ?

Topic: Areas of Similar Triangles

9 : 1

2 : 3

6 : 9

4 : 5

None

35.

If P and Q are the points on side CA and CB respectively of △ABC, right angled at C, Then $ \displaystyle \left( {\text{A}{{\text{Q}}^{2}}+\text{B}{{\text{P}}^{2}}} \right)$ will be equal to:

Topic: Pythagoras Theorem

$ \displaystyle \left( {\text{A}{{\text{B}}^{2}}+\text{P}{{\text{Q}}^{2}}} \right)$

$ \displaystyle \left( {\text{B}{{\text{C}}^{2}}+\text{C}{{\text{A}}^{2}}} \right)$

$ \displaystyle \left( {\text{A}{{\text{B}}^{2}}+\text{B}{{\text{C}}^{2}}} \right)$

$ \displaystyle \left( {\text{P}{{\text{C}}^{2}}+\text{Q}{{\text{C}}^{2}}} \right)$

None

36.

The corresponding sides of two similar triangles are in the ratio of 2:3. If the area of the small triangle is 48 sq.cm, then the area of large triangle is: of the circle is 13 cm, What is the value of distance between the two chords?

Topic: Areas of Similar Triangles

142 cm²

125 cm²

108 cm²

190 cm²

None

37.

In the given figure PQ is parallel to AB and PR is parallel to AC. By using which of the following theorems it can be proved that QR is parallel to BC?

Topic: Basic Proportionality Theorem

Basic Proportionality Theorem

Thales Theorem

Converse of Basic Proportionality Theorem

All of the above

None

38.

In the given figure, ABC is a triangle in which AB = AC. Points D and E are points on the sides AB and AC respectively such that AD = AE. Then, the points B, C, E and D will be called as:

Topic: Isosceles Triangle Properties

Concyclic points

Collinear points

Concurrent points

Non-Coplanar points

None

39.

All circles are _______. What is the correct answer from the given option?

Topic: Properties of Circles

Congruent

Similar

Isosceles

Equilateral

None

40.

All squares are ________. What is the correct answer from the given option?

Topic: Properties of Squares

Similar

Proportional

Congruent

Equal

None

1 out of 40

Time's up

Class 10 Practice – Level 1 – Triangles

Welcome back