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Triangles — Maths STD 9 — Question

Gujarat BoardEnglish MediumSTD 9MathsTriangles1 Mark
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:
  • A
    Isosceles but not congruent
  • B
    Isosceles and congruent
  • C
    Congruent but not isosceles
  • D
    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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