If in two triangles - ABC and - PQR-AB-QR-BC-PR-CA-PQ- thenA - PQR - CABB - PQR - ABCC - CBA - PQRD - BCA - PQR

Answer: (A) nbsp;Δ PQR ∼Δ nbsp;CAB Given that in Δ nbsp;ABC and Δ nbsp;PQR,AB/QR=BC/PR=CA/PQ.This shows that sides of one triangle are proportional t ...

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Byju's Answer

Standard X

Mathematics

Relation between Areas and Sides of Similar Triangles

If in two tri...

Question

If in two triangles $Δ A B C a n d Δ P Q R, \frac{A B}{Q R} = \frac{B C}{P R} = \frac{C A}{P Q}$ , then

(A) $Δ P Q R \sim Δ C A B$
(B) $Δ P Q R \sim Δ A B C$
(C) $Δ C B A \sim Δ P Q R$
(D) $Δ B C A \sim Δ P Q R$

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Solution

Answer: (A) $Δ P Q R \sim Δ C A B$

Given that in $Δ A B C a n d Δ P Q R, \frac{A B}{Q R} = \frac{B C}{P R} = \frac{C A}{P Q}$ .This shows that sides of one triangle are proportional to the sides of the other triangle.
If the sides of one triangle are proportional to the sides of the other triangle, then their corresponding angles are also equal. So by SSS similarity rule, the given triangles are similar.
i.e., $Δ C A B \sim Δ P Q R$
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Similar questions

Q. If in ∆ABC and ∆PQR, we have:

\frac{A B}{Q R} = \frac{B C}{P R} = \frac{C A}{P Q}

, then
(a) ∆PQR ∼ ∆CAB
(b) ∆PQR ∼ ∆ABC
(c) ∆CBA ∼ ∆PQR
(d) ∆BCA ∼ ∆PQR

Choose the correct answer in each of the following:

$If AB = QR, BC = RP and CA = PQ then which of the following holds? (a) Δ A B C ≅ Δ P Q R (b) Δ C B A ≅ Δ P Q R (c) Δ C A B ≅ Δ P Q R (d) Δ B C A ≅ Δ P Q R$