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This mock test of Test: Problems On Similar Triangles for Class 10 helps you for every Class 10 entrance exam.
This contains 10 Multiple Choice Questions for Class 10 Test: Problems On Similar Triangles (mcq) to study with solutions a complete question bank.
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QUESTION: 1

Consider the triangle shown in the figure where BC = 12 cm, Db = 9 cm, CD = 6 cm and What is the ratio of the perimeter of the triangle ADC to that of the triangle BDC?

Solution:

Here, ∠ACB = c+180-(2c-b) = 180-(b+c)

So, We can say that Δ BCD and &delta ABC will be similar.

According to property of similarity,

AB/12 = 12/9

Hence,

AB = 16

AC/6 = 12/9

AC = 8

Hence, AD = 7 and AC = 8

Now,

Perimeter of Δ ADC / Perimeter of ΔBDC,

= (6+7+8)/(9+6+12)

= 21/27 = 7/9.

QUESTION: 2

In ΔPQR, ∠P = 60°, ∠Q = 50°. Which side of the triangle is the longest ?

Solution:

QUESTION: 3

If ABC and PQR are similar triangles in which ∠ A = 47^{0} and ∠ Q = 83^{0}, then ∠ C is:

Solution:

QUESTION: 4

In the given figure, T and B are right angles. If the lengths of AT, BC and AS (in centimeters) are 15, 16 and 17 respectively, then the length of TC (in centimeters) is:

Solution:

QUESTION: 5

In the adjoining figure, AD = 2 cm, DB = 3 cm, AE = 5 cm and DE || BC, then find EC.

Solution:

QUESTION: 6

In an equilateral triangle ABC, if AD ⊥ BC. Then

Solution:

∆ ABC, in which sides are AB=BC= AC= a units and AD is perpendicular to BC ,

In ∆ADB ,

AB²= AD²+ BD² (by Pythagoras theorem)

a² = AD² + (a/2)² [BD= 1/2BC, since in an equilateral triangle altitude AD is perpendicular bisector of BC ]

a²- a²/4 =AD²

⇒ ( 4a²-a²)/4 = AD²

⇒ 3a² /4 = AD²

⇒ 3AB²/4= AD² [ AB= a]

⇒ 3AB²= 4AD²

QUESTION: 7

In two triangles ABC and PQR,Given that ∠A = ∠R and ∠B = ∠Q, which of the following is true?

Solution:

∠A = ∠R and ∠B = ∠Q

The names of triangles are written in such a manner in which the Angles are correspondingly equal which means that the vertices at which the angles of the two triangles are equal is placed accordingly. So since the the angle A and Angle R are equal and Angle B and Angle D are equal we have ΔABC - ΔRQP

QUESTION: 8

Triangles ABC, DEF are similar, ∠A = 75° , ∠B = 85° so ∠F = ?

Solution:

QUESTION: 9

A vertical stick 30 m long casts a shadow 15 m long on the ground. At the same time, a tower casts a shadow 75 m long on the ground. The height of the tower is:

Solution:

QUESTION: 10

Given two triangles ABC and PQR such that, AB = 2 cm, PQ = 3cm, ∠B = ∠Q BC = 5 cm, QR = 7.5 cm. AG and PS are medians . Find AG/PS = ?

Solution:

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