If -ABC - -EDF and -ABC is not similar to -DEF- then which of the following is not true- -a- BC - EF - AC - FD -b- AB - EF - AC - DE -c- BC - DE - AB - EF -d- BC - DE - AB - FD - Maths Q-A

Explanation of correct option,Option C: BC·DE = AB·EFGiven: Δ ABC Δ EDFThus, AB/ED = BC/DF = AC/EFConsidering, AB/ED = BC/DF⇒ AB·DF = BC·EDSo, the ...

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Byju's Answer

Standard X

Mathematics

Basic Proportionality Theorem

If ΔABC ~ ΔED...

Question

If $Δ A B C ~ Δ E D F$ and $Δ A B C$ is not similar to $Δ D E F$ , then which of the following is not true?

$B C times E F space equals space A C times F D$

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$A B \cdot E F = A C \cdot D E$

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$B C \cdot D E = A B \cdot E F$

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$B C \cdot D E = A B \cdot F D$

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Solution

The correct option is C
$B C \cdot D E = A B \cdot E F$

Explanation of correct option,
Option $C$ : $B C \cdot D E = A B \cdot E F$
Given: $Δ A B C ~ Δ E D F$
Thus, $\frac{A B}{E D} = \frac{B C}{D F} = \frac{A C}{E F}$
Considering, $\frac{A B}{E D} = \frac{B C}{D F}$
$\Rightarrow$ $A B \cdot D F = B C \cdot E D$
So, the given statement is not true.
Hence, option $C$ is the correct answer.
Explanation of incorrect option
Option $A$ : $B C \cdot E F = A C \cdot F D$
Considering, $\frac{B C}{D F} = \frac{A C}{E F}$
$\Rightarrow$ $B C \cdot E F = A C \cdot D F$
Which is same as the given statement and hence is true.
Hence, option $A$ is incorrect.
Option $B$ : $A B \cdot E F = A C \cdot D E$
Considering, $\frac{A B}{E D} = \frac{A C}{E F}$
$\Rightarrow$ $A B \cdot E F = A C \cdot E D$
Which is same as the given statement and hence is true.
Hence, option $B$ is incorrect.
Option $D$ : $B C \cdot D E = A B \cdot F D$
Considering, $\frac{B C}{D F} = \frac{A B}{E D}$
$\Rightarrow$ $B C \cdot E D = A B \cdot D F$
Which is same as the given statement and hence is true.
So, option $D$ is incorrect.
Hence, option $C$ is the correct option.

Suggest Corrections

Similar questions

Q. Select the appropriate alternative.
(1) In ∆ABC and ∆PQR, in a one to one correspondence

\frac{AB}{QR} = \frac{BC}{PR} = \frac{CA}{PQ}

then

(A) ∆PQR ~ ∆ABC
(B) ∆PQR ~ ∆CAB
(C) ∆CBA ~ ∆PQR
(D) ∆BCA ~ ∆PQR

(2) If in ∆DEF and ∆PQR, ∠D ≅ ∠Q, ∠R ≅ ∠E then which of the following statements is false?

(A)

\frac{EF}{PR} = \frac{DF}{PQ}

(B)

\frac{DE}{PQ} = \frac{EF}{RP}

(C)

\frac{DE}{QR} = \frac{DF}{PQ}

(D)

\frac{EF}{RP} = \frac{DE}{QR}

(3) In ∆ABC and ∆DEF ∠B = ∠E, ∠F = ∠C and AB = 3DE then which of the statements regarding the two triangles is true ?
(A)The triangles are not congruent and not similar
(B) The triangles are similar but not congruent.
(C) The triangles are congruent and similar.
(D) None of the statements above is true.

(4) ∆ABC and ∆DEF are equilateral triangles, A (∆ABC) : A (∆DEF) = 1 : 2
If AB = 4 then what is length of DE?
(A)

2 \sqrt{2}

(B) 4
(C) 8
(D)

4 \sqrt{2}

(5) In the given figure, seg XY || seg BC, then which of the following statements is true?

(A)

\frac{AB}{AC} = \frac{AX}{AY}

(B)

\frac{AX}{XB} = \frac{AY}{AC}

(C)

\frac{AX}{YC} = \frac{AY}{XB}

(D)

\frac{AB}{YC} = \frac{AC}{XB}

Q. If ∆ABC and ∆DEF are two triangles such that

\frac{AB}{DE} = \frac{BC}{EF} = \frac{CA}{FD} = \frac{3}{4}

, then write Area (∆ABC) : Area (∆DEF)

Question 42

If for $Δ A B C$ and $Δ D E F$ , the correspondence $C A B \leftrightarrow E D F$ gives a congruence, then which of the following is not true?

a) AC = DE
b) AB = EF
c) $∠ A = ∠ D$
d) $∠ C = ∠ E$

If $Δ A B C ≅ Δ P Q R a n d Δ A B C is not congruent to Δ R P Q, then which of the following is not true:$

Q. ∆ABC and ∆DEF are equilateral triangles. If A(∆ABC) : A (∆DEF) = 1 : 2 and AB = 4, find DE.

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

If $Δ A B C ~ Δ E D F$ and $Δ A B C$ is not similar to $Δ D E F$ , then which of the following is not true?