1. **State the problem:** Determine if the given triangles are right triangles based on their side lengths. 2. **Recall the Pythagorean theorem:** For a triangle with sides $a$, $b$, and hypotenuse $c$, the triangle is right-angled if and only if $$a^2 + b^2 = c^2$$ where $c$ is the longest side. 3. **Triangle (a) with sides 65, 72, and 97:** - Identify the longest side: $97$ - Check if $$65^2 + 72^2 = 97^2$$ Calculate each square: $$65^2 = 4225$$ $$72^2 = 5184$$ $$97^2 = 9409$$ Sum of squares of shorter sides: $$4225 + 5184 = 9409$$ Since $$9409 = 9409$$, the Pythagorean theorem holds. 4. **Triangle (b) with sides 5, $\sqrt{26}$, and unknown hypotenuse:** - Since the hypotenuse is not labeled, assume the longest side is the hypotenuse. - Calculate squares of known sides: $$5^2 = 25$$ $$\left(\sqrt{26}\right)^2 = 26$$ Sum: $$25 + 26 = 51$$ - The hypotenuse squared should be 51 for the triangle to be right-angled. - Since the hypotenuse is not given, we cannot confirm if the triangle is right-angled without that length. **Final answers:** - Triangle (a) is a right triangle. - Triangle (b) cannot be determined as right triangle without the hypotenuse length.