4th Class Mental Ability Geometry Question Bank Geometry

  • question_answer
    Triangle ABC given below is a right-angled isosceles triangle in which \[\angle \text{BAC}=90{}^\circ \]. Which one of the following relations is true?

    A) \[\angle \text{ABC}+\angle \text{ACB}=\angle \text{BAC}\]

    B) \[\text{AB+AC}=\text{BC}\]

    C) \[\angle \text{ABC}=\angle \text{ACB}=30{}^\circ \]

    D)  \[\text{BC}=2\times \text{AB}\]

    E) None of these

    Correct Answer: A

    Solution :

    Explanation: Option (a) is correct Since, triangle ABC is right-angled isosceles triangle, Therefore, \[\angle \text{ABC}=\angle \text{ACB}=45{}^\circ \] and AB = AC Now, In option (a); \[\angle \text{ABC}+\angle \text{ACB}=45{}^\circ +45{}^\circ \] \[=90{}^\circ =\angle \text{BAC}\] In option (b); Sum of any two sides of a triangle is always greater than its third side. In option (c); \[\angle \text{ABC}=\angle \text{ACB}=45{}^\circ \] (not \[30{}^\circ \]) In option (d); BC is smaller than (AB + AC) or (AB + AB) or 2AB

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