Question 4 If in two and - ABC and - PQR - AB - QR - BC - PR - CA - PQ- thenA - PQR - CABB - PQR - ABCC - CBA - PQRD - BCA - PQR

(A) Δ PQR ∼Δ CAB Given, in two Δ ABC and Δ PQR,AB/QR=BC/PR=CA/PQ, Which shows that sides of one triangle are proportional to the side of the other trian ...

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Standard VIII

Mathematics

Converse of BPT

Question 4 If...

Question

Question 4
If in two and $Δ A B C a n d Δ P Q R, \frac{A B}{Q R} = \frac{B C}{P R} = \frac{C A}{P Q}$ , 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

(A) $Δ P Q R \sim Δ C A B$

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

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Similar questions

Q. Question 4
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

Q. Question 2
If AB = QR, BC+PR and CA = PQ, then
(A)

Δ A B C ≅ Δ P Q R

(B)

Δ C B A ≅ Δ P Q R

(C)

Δ B A C ≅ Δ B C A

(D)

Δ P Q R ≅ Δ B C A

In $Δ$ ABC and $Δ$ PQR, AB = 4 cm, BC = 5 cm, AC = 6 cm and PQ = 4 cm, QR = 5 cm, PR = 6 cm, then

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:

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

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Question 4 If in two and ΔABC and ΔPQR,ABQR=BCPR=CAPQ, then (A) ΔPQR∼ΔCAB (B) ΔPQR∼ΔABC (C) ΔCBA∼ΔPQR (D) ΔBCA∼ΔPQR

(A) ΔPQR∼ΔCAB Given, in two ΔABC and ΔPQR,ABQR=BCPR=CAPQ, Which shows that sides of one triangle are proportional to the side of the other triangle, then their corresponding angles are also equal, so by SSS similarity , triangles are similar. i.e., ΔCAB∼ΔPQR

Question 4
If in two and $Δ A B C a n d Δ P Q R, \frac{A B}{Q R} = \frac{B C}{P R} = \frac{C A}{P Q}$ , 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) $Δ B C A \sim Δ P Q R$