• # 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

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