In and , it is given that AB = AC, = and = . Then, the two triang… - Vidyadip

MCQ

In $\triangle\text{ABC}$ and $\triangle\text{PQR},$ it is given that $AB = AC, \angle\text{C}=\angle\text{P}$ and $\angle\text{B}=\angle\text{Q}.$ Then, the two triangles are:

✓
Isosceles but not congruent
B
Isosceles and congruent
C
Congruent but not isosceles
D
Neither congruent nor isosceles

✓

Answer

Correct option: A.

Isosceles but not congruent

In $\triangle\text{ABC}$ and $\triangle\text{PQR},$
$\text{AB = AC}$
$\Rightarrow\angle\text{B}=\angle\text{C}$
Since $\angle\text{C}=\angle\text{P}$ and $\angle\text{B}=\angle\text{Q}$
$\Rightarrow\angle\text{P}=\angle\text{Q}$
$\Rightarrow\text{RQ = RP}$
So, the two triangle are isosceles.
But it is not possible to prove them congruent.

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