Important Questions: Triangles


10 Questions MCQ Test Online MCQ Tests for Class 10 | Important Questions: Triangles


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Attempt Important Questions: Triangles | 10 questions in 10 minutes | Mock test for Class 10 preparation | Free important questions MCQ to study Online MCQ Tests for Class 10 for Class 10 Exam | Download free PDF with solutions
QUESTION: 1

In Fig. 7.4, ∠BAC = 90° and AD ⊥ BC. Then,

Solution:

QUESTION: 2

In the given figure, AD/BD = AE/EC and ∠ADE = 70°, ∠BAC = 50°, then angle ∠BCA =

Solution:

The correct option is Option D.

By using angle sum property, we find third angle

AED = 180° - (70°+50°) = 60°

and DE ll BC 

So, by corresponding angle, we get the value of BCA = 60°.

QUESTION: 3

If ΔABC ~ ΔEDF and ΔABC is not similar to ΔDEF, then which of the following is not true?

Solution:

Since △ABC~△EDF

Then, AB/ED = BC/DF = AC/EF

1) BC/DF = AC/EF

⇒BC.EF=AC.FD   

So, A) is true

 

2) AB/ED = AC/EF

⇒AB.EF=AC.DE     

So,B) is true

 

3) AB/ED = BC/DF

BC.DE=AB.EF    

So, D) is true

 

Therefore, Option C is not true

QUESTION: 4

Which pair of the given quadrilaterals is similar?

Solution:

Quadrilaterals are similar if their angles are equal and corresponding sides are proportional.

QUESTION: 5

D and E are respectively the points on the sides AB and AC of a triangle ABC such that AD = 3 cm, BD = 5 cm, BC = 12.8 cm and DE || BC. Then length of DE (in cm) is

Solution:

GIVEN: In  Δ ABC, D and E are points on AB and AC , DE ||  BC and  AD = 2.4 cm, AE = 3.2 cm, DE = 2 cm and BE = 5 cm.
In Δ ADE and Δ ABC,
∠ADE =∠ABC    (corresponding angles)
[DE || BC, AB is transversal]
∠AED =∠ACB     (corresponding angles)
[DE || BC, AC is transversal]
So, Δ ADE  ~ Δ ABC      (AA similarity)
Therefore, AD/AB = AE/AC = DE/BC
[In similar triangles corresponding sides are proportional]
AD/AB = DE/BC
2.4/(2.4+DB)  = 2/5
2.4 × 5  = 2(2.4+ DB)
12 = 4.8 + 2DB
12 - 4.8  = 2DB
7.2 = 2DB
DB = 7.2/2  
DB = 3.6 cm
Similarly, AE/AC = DE/BC
3.2/(3.2+EC) = 2/5
3.2 × 5 = 2(3.2+EC)
16 = 6.4 + 2EC
16 - 6.4 = 2EC
9.6 = 2EC
EC = 9.6/2
EC = 4.8 cm
Hence,BD = 3.6 cm and CE = 4.8 cm.

QUESTION: 6

If in two triangles ABC and PQR, AB/QR = BC/PR = CA/PQ , then

Solution:


Then, ΔCAB ~ ΔPQR

QUESTION: 7

If ΔPRQ ~ ΔXYZ, then

Solution:

Since the two triangles are similar, therefore, they will have their corresponding angles congruent and the corresponding sides in proportion.

QUESTION: 8

Match the column:

Solution:

Properties of triangles.

QUESTION: 9

In triangles ABC and DEF, ∠B = ∠E, ∠F = ∠C and AB = 3DE. Then, the two triangles are

Solution:

to be congruent, the conditions are
S S S - three sides
S A S - two sides and the included angle
A S A - two angles and one side
R H S - R H S - Right angle, Hypotenuse and one side
But to be similar,
A A A means 3 angles
A A means only two angles ....
in both triangles should be equal.
In the problem, equality of two angles is given, but equality of sides is not given.
So, given triangles are not congruent.
But they are similar.

QUESTION: 10

ABC and BDE are two equilateral triangles such that D is mid-point of BC. Ratio of the areas of triangles ABC and BDE is

Solution:


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