Question 3If - ABC - EDF and - ABC is not similar to - DEF- then which of the following is not true-A BC-EF - AC-FDB AB-EF - AC-DEC BC-DE - AB-EFD BC-DE - AB-FD

(C) BC.DE = AB.EF Given, Δ ABC∼Δ EDF ∴ AB/ED=BC/DF=AC/EF Taking first two terms, we get AB/ED=BC/DF ⇒ AB.DF = BC.ED Or BC.DE = AB.FD Taking last two ter ...

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Standard X

Mathematics

Basic Proportionality Theorem

Question 3If ...

Question

Question 3
If $Δ A B C \sim Δ E D F a n d Δ A B C$ is not similar to $Δ D E F$ , 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

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Solution

(C) BC.DE = AB.EF

Given, $Δ A B C \sim Δ E D F$
$∴ \frac{A B}{E D} = \frac{B C}{D F} = \frac{A C}{E F}$

Taking first two terms, we get
$\frac{A B}{E D} = \frac{B C}{D F}$
$\Rightarrow A B . D F = B C . E D$
Or BC.DE = AB.FD

Taking last two terms, we get
$\frac{B C}{D F} = \frac{A C}{E F}$
$\Rightarrow B C . E F = A C . D F$
Or BC.EF = AC.FD

Taking first and last terms, we get
$\frac{A B}{E D} = \frac{A C}{E F}$
$\Rightarrow A B . E F = A C . E D$
Or AB.EF = AC.DE

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Similar questions

Q. Question 3
If

Δ A B C \sim Δ E D F a n d Δ A B C

is not similar to

Δ D E F

, 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

Q. In the given figure, AE = DB, CB = EF and ∠ABC = ∠FED. Then, which of the following is true?
(a) ∆ABC ≅ ∆DEF
(b) ∆ABC ≅ ∆EFD
(c) ∆ABC ≅ ∆FED
(d) ∆ABC ≅ ∆EDF

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) $∠ C = ∠ E$

Q. If the correspondence

A B C \leftrightarrow E F D

is a similarity in

Δ A B C

and

Δ D E F,

then _____ of the following is not true.

In $Δ A B C, D$ is the midpoint of BC and $A E ⊥ B C$ . If $A C > A B$ , show that $A B^{2} = A D^{2} - B C . D E + \frac{1}{4} B C^{2}$ .

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Question 3 If ΔABC∼ΔEDF and ΔABC is not similar to ΔDEF, 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

(C) BC.DE = AB.EF Given, ΔABC∼ΔEDF ∴ ABED=BCDF=ACEF Taking first two terms, we get ABED=BCDF ⇒ AB.DF=BC.ED Or BC.DE = AB.FD Taking last two terms, we get BCDF=ACEF ⇒ BC.EF=AC.DF Or BC.EF = AC.FD Taking first and last terms, we get ABED=ACEF ⇒ AB.EF=AC.ED Or AB.EF = AC.DE

Question 3
If $Δ A B C \sim Δ E D F a n d Δ A B C$ is not similar to $Δ D E F$ , 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