Class 10 Practice – Level 2 – Set 1 – Triangles

Total questions: 25

ABCD is a trapezium in which AB ∣∣ DC and its diagonals intersect each other at the point O. So, $ \displaystyle \dfrac{{\text{AO}}}{{\text{BO}}}$ will be equal to:

Topic: Properties of Trapezium

$ \displaystyle \dfrac{{\text{CO}}}{{\text{DO}}}$

$ \displaystyle \dfrac{{\text{DO}}}{{\text{CO}}}$

$ \displaystyle \dfrac{{\text{AB}}}{{\text{DC}}}$

$ \displaystyle \dfrac{{\text{BC}}}{{\text{AD}}}$

None

The diagonals of a quadrilateral ABCD intersect each other at the point O such that $ \displaystyle \dfrac{{\text{AO}}}{{\text{BO}}}=\dfrac{{\text{CO}}}{{\text{DO}}}$. The quadrilateral ABCD will be a:

Topic: Properties of Intersecting Diagonals in a Quadrilateral

Kite

Trapezium

Parallelogram

None of the above

None

In the given figure, $ \displaystyle \dfrac{{\text{QR}}}{{\text{QS}}}=\dfrac{{\text{QT}}}{{\text{PR}}}$ and ∠1 = ∠2. Will the triangles △PQS and △TQR will be congruent?

Topic: Congruence of Triangles

Yes

No relation exists

Incomplete information

None

S and T are points on sides PR and QR of △ PQR such that ∠P = ∠RTS. △ RPQ ∼ △ RTS can be proved using:

Topic: Similar Triangles

AA criterion

SAS criterion

AAA criterion

ASA criterion

None

In the given figure., if △ ABE ≅ △ ACD, the △ ADE ∼ △ ABC can be proved using:

Topic: Similar Triangles

SSS criterion

AAA criterion

ASA criterion

SAS criterion

None

E is a point on the side AD produced of a parallelogram ABCD and BE intersects CD at F. △ABE ∼ △CFB can be proved using:

Topic: Similar Triangles

ASA criterion

AA criterion

SAS criterion

SSS criterion

None

△ABC and △BDE are two equilateral triangles such that D is the mid-point of BC. The ratio of the areas of triangles △ABC and △BDE will be:

Topic: Areas of Similar Triangles

2:1

1:2

4:1

1:4

None

The sides of two similar triangles are in the ratio 4 : 9. The ratio of the areas of these triangles will be:

Topic: Areas of Similar Triangles

2:3

4:9

7:1

16:81

None

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

Topic: Application of Pythagoras Theorem

8 m

4 m

6 m

2 m

None

10.

A guy wire attached to a vertical pole of height 18 m is 24 m long and has a stake attached to the other end. How far from the base of the pole should the stake be driven so that the wire will be taut?

Topic: Application of Pythagoras Theorem

$ \displaystyle \text{7}\sqrt{2}\text{ m}$

9 m

$ \displaystyle \text{6}\sqrt{7}\text{ m}$

$ \displaystyle \text{7}\sqrt{9}\text{ m}$

None

11.

An aeroplane leaves an airport and flies due north at a speed of 1000 km per hour. At the same time, another aeroplane leaves the same airport and flies due west at a speed of 1200 km per hour. How far apart will be the two planes after $ \displaystyle 1\dfrac{1}{2}$ hours?

Topic: Relative Motion in Two Dimensions

500 km

$ \displaystyle 300\sqrt{{61}}$ km

$ \displaystyle 200\sqrt{{41}}$ km

400 km

None

12.

Two poles of heights 6 m and 11 m stand on a plane ground. If the distance between the feet of the poles is 12 m. What is the distance between their tops?

Topic: Distance Between Two Points

13 m

16 m

21 m

32 m

None

13.

In an equilateral triangle, three times the square of one side is equal to:

Topic: Properties of an Equilateral Triangle

Four times the square of one of its altitudes

Twice of its altitudes

Four times of one of its altitudes

Six times the square of one of its altitudes

None

14.

In △ ABC, AB = $ \displaystyle \text{6}\sqrt{3}\text{ cm}$, AC = 12cm and BC = 6cm. The value of ∠B is:

Topic: Application of the Law of Cosines

120°

60°

90°

45°

None

15.

In a ΔABC, AD is the bisector of ∠A. If AB = 5.6cm, BD = 3.2cm and BC = 6cm, find AC.

Topic: Angle Bisector Theorem

2.3 cm

4.9 cm

5.3 cm

7.5 cm

None

16.

In a ΔABC, AD is the bisector of ∠A. If AB = 6.4cm, AC = 8cm and BD = 5.6cm, find DC.

Topic: Angle Bisector Theorem

7 cm

10 cm

12 cm

15 cm

None

17.

In a ΔABC, AD is the bisector of ∠A. If AB = 10cm, AC = 14cm and BC = 6cm, find BD and DC.

Topic: Angle Bisector Theorem

5.5 cm, 2.5 cm

6.4 cm, 3.5 cm

2.5 cm, 3.5 cm

2.4 cm, 2.5 cm

None

18.

D and E are points on the sides AB and AC respectively of a ΔABC such that DE∣∣BC. What is the value of x, when AD = xcm , DB = (x − 2)cm, AE = (x + 2)cm and EC = (x − 1)cm.

Topic: Basic Proportionality Theorem

4 cm

8 cm

10 cm

15 cm

None

19.

D and E are points on the sides AB and AC respectively of a ΔABC such that DE∣∣BC. If AB = 13.3cm, AC = 11.9cm and EC = 5.1cm, find AD.

Topic: Basic Proportionality Theorem

10 cm

4.2 cm

3.6 cm

7.6 cm

None

20.

D and E are points on the sides AB and AC respectively of a ΔABC. Determine the relation between DE and BC if AD = 7.2cm, AE = 6.4cm, DB = 12cm and EC = 10cm?

Topic: Basic Proportionality Theorem

Parallel

Not parallel

Intersecting

Perpendicular

None

21.

D and E are points on the sides AB and AC respectively of a ΔABC such that DE∣∣BC. What is the value of x, when AD = 4cm, DB = (x − 4)cm, AE = 8cm and EC = (3x − 19)cm?

Topic: Basic Proportionality Theorem

9 cm

7 cm

11 cm

16 cm

None

22.

The line segment which joins the midpoints of the oblique sides of a trapezium is parallel to the parallel sides. Is it true or not?

Topic: Midpoint Theorem

True

False

Cannot be determined

Incomplete information

None

23.

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

Topic: Basic Proportionality Theorem

8 cm, 11.3 cm

10.2 cm, 6.5 cm

12.5 cm, 6.5 cm

8 cm, 12.5 cm

None

24.

In a ΔABC, AD is the bisector of ∠A. If AB = 5.6cm, AC = 4cm and DC = 3cm, What is the value of BC.

Topic: Angle Bisector Theorem

4.1 cm

2.3 cm

5.7 cm

7.2 cm

None

25.

The corresponding sides of two similar triangles ABC and DEF are BC=9.1cm and EF=6.5cm. If the perimeter of ΔDEF is 25cm, then the perimeter of ΔABC will be:

Topic: Criteria for Similarity Triangles

25 cm

35 cm

45 cm

55 cm

None

1 out of 25

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Class 10 Practice – Level 2 – Set 1 – Triangles

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