$I n Δ A B C a n d Δ P Q R, it is given that AB = AC, ∠ C = ∠ P a n d ∠ B = ∠ Q . Then, the two triangles are$

congruent but not isosceles

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isosceles and congruent

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isosceles but not congruent

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neither congruent nor isosceles

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Solution

The correct option is C isosceles but not congruent
Correct option is A).
In △ABC and △PQR,
∠C = ∠P (Given)
∠B = ∠Q (Given)
∠A = ∠R (Third angle of the triangle)
△ABC ∼ △RQP

Also, given, AB = AC
Thus, ∠B = ∠C (Isosceles triangle Property)
But, ∠C = ∠P and ∠B = ∠Q.
Hence, ∠Q = ∠P
or
PR = QR

Thus, both the triangles are Isosceles but not congruent.

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I n Δ A B C a n d Δ P Q R, it is given that AB = AC, ∠ C = ∠ P a n d ∠ B = ∠ Q . Then, the two triangles are

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Δ A B C

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Q. Match the column.

1. In $Δ A B C$ and $Δ P Q R$ , $\frac{A B}{P Q} = \frac{A C}{P R}, ∠ A = ∠ P$	(a) AA similarity criterion
2. In $Δ A B C$ and $Δ P Q R$ , $∠ A = ∠ P, ∠ B = ∠ Q$	(b) SAS similarity criterion
3. In $Δ A B C$ and $Δ P Q R$ , $\frac{A B}{P Q} = \frac{A C}{P R} = \frac{B C}{Q R}$ $∠ A = ∠ P$	(c) SSS similarity criterion
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In ΔABC and ΔPQR, it is given that AB = AC, ∠C=∠P and ∠B=∠Q.Then, the two triangles are

$I n Δ A B C a n d Δ P Q R, it is given that AB = AC, ∠ C = ∠ P a n d ∠ B = ∠ Q . Then, the two triangles are$