Test: Criteria For Similar Triangles


10 Questions MCQ Test Mathematics (Maths) Class 10 | Test: Criteria For Similar Triangles


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QUESTION: 1

If ΔDEF ~ ΔABC and DE = AB, what is the relation between the two triangles?​

Solution:

Since DE=AB means that there ratio is 1 which means corresponding sides are equal.Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion . In other words, similar triangles are the same shape, but not necessarily the same size. The triangles are congruent if, in addition to this, their corresponding sides are of equal length.So they are congruent.

QUESTION: 2

In the following figure, find the value of x.

Solution:

The triangles are similar by SAS criterion, So we have, Angle A+Angle B + Angle C=180
x=180-30-80=70 degrees 

QUESTION: 3

In the figure given below, if DE || BC, then x equals :

Solution:

We have Angle ADE= Angle ABC
And ANGLE A is common, So by AA criterion of similarity the two triangles are similar so AD/AB=DE/BC
x=5*4/3=6.7

QUESTION: 4

Given that ΔABC ~ ΔDEF and AB = 2cm , BC = 3cm, DE = 4cm, EF = 6cm , If DF = 8cm, then AC = ?​

Solution:

We have 
=2/4=½
So, 
AC=8/2=4cm

QUESTION: 5

If ΔPQR ~ ΔXYZ, ∠Q = 50°, ∠R = 70° then ∠X is equal to :​

Solution:
QUESTION: 6

Given that ΔABC ~ ΔDEF ∠A = 50°, ∠C = 35° ∠E = ?

Solution:
QUESTION: 7

In the given figure perpendiculars are dropped on the common base BD of the given two triangles. AE = 2cm, CF = 3cm  

Solution:

Area of triangle = 1/2 *base*height
Area of ABD=1/2 *BD*2
Area of  BDC=1/2*BD*3

QUESTION: 8

In the given figure ΔABC ~ ΔBDC = 90° each. Choose the correct similarity from the given choices.

Solution:

We have Angle C common and Angle B = Angle D
So in similarity we write the name of the triangle in such an order in which the corresponding alphabets denote equal angles . this means that ΔABC ~ ΔBDC that says Angle A = Angle B, Angle B = Angle D, and Angle C = Angle C

QUESTION: 9

ΔABC ~ ΔDEF Perimeter (ΔABC) = 15 cm, Perimeter (DEF) = 25 cm.If AB = 6 cm, then find DE.

Solution:

Ratios of perimeter of similar triangles are equal to the ratio of their sides.
So Perimeter of ABC/perimeter of DEF=15/25=⅗
AB/DE=⅗
DE=6*5/3=10

QUESTION: 10

In the given figure use the similarity of the given triangles to find the value of BD,

ΔABC ~ ΔBDC,  ∠BDC = ∠ABC = 90°, AB = 3, BC = 4,AD = 2, BD = ?

Solution:

Solution : 

The correct option is Option C.

∆ ABC ~ ∆ BDC = AD/AB = BD/BC = ⅔ = BD/4 = BD = 8/3

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