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Congruence of Triangles and Inequalities in a Triangle — Maths STD 9 — Question

Gujarat BoardEnglish MediumSTD 9MathsCongruence of Triangles and Inequalities in a Triangle1 Mark
Question
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:
  1. Isosceles but not congruent
  2. Isosceles and congruent
  3. Congruent but not isosceles
  4. Neither congruent nor isosceles
✓

Answer

  1. Isosceles but not congruent

Solution:

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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