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Standard VII

Mathematics

ASA Criteria for Congruency

If A B=Q R, B...

Question

If AB = QR, BC = RP and CA = PQ, then which of the following holds?
(a) ∆ABC ≅ ∆PQR
(b) ∆CBA ≅ ∆PQR
(c) ∆CAB ≅ ∆PQR
(d) ∆BCA ≅ ∆PQR

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Solution

(c) $∆ C A B ≅ ∆ P Q R$
As,
AB = QR, (given)
BC = RP, (given)
CA = PQ (given)

∴ $∆ C A B ≅ ∆ P Q R$

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Similar questions

Choose the correct answer in each of the following:

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

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

Q. 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

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

In $Δ A B C$ , AB = 4 cm, BC = 5 cm, AC = 6 cm. In $Δ P Q R$ , PQ = 4 cm, QR = 5 cm, PR = 6 cm. Which of the following is true?

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If AB = QR, BC = RP and CA = PQ, then which of the following holds? (a) ∆ABC ≅ ∆PQR (b) ∆CBA ≅ ∆PQR (c) ∆CAB ≅ ∆PQR (d) ∆BCA ≅ ∆PQR

(c) ∆CAB≅∆PQR As, AB = QR, (given) BC = RP, (given) CA = PQ (given) ∴ ∆CAB≅∆PQR

If AB = QR, BC = RP and CA = PQ, then which of the following holds?
(a) ∆ABC ≅ ∆PQR
(b) ∆CBA ≅ ∆PQR
(c) ∆CAB ≅ ∆PQR
(d) ∆BCA ≅ ∆PQR

(c) $∆ C A B ≅ ∆ P Q R$
As,
AB = QR, (given)
BC = RP, (given)
CA = PQ (given)

∴ $∆ C A B ≅ ∆ P Q R$