Question

which statements are true about triangle qrs? select three options. the side opposite ∠q is \\(\overline{rs}\\). the side opposite ∠r is \\(\overline{rq}\\). the hypotenuse is \\(\overline{qr}\\). the side adjacent to ∠r is \\(\overline{sq}\\). the side adjacent to ∠q is \\(\overline{qs}\\).

Explanation:

1. For a right triangle, the side opposite an angle does not form the angle. ∠Q is formed by $\overline{QS}$ and $\overline{QR}$, so the opposite side is $\overline{RS}$.
2. The hypotenuse is the side opposite the right angle (∠S), so it is $\overline{QR}$.
3. The side adjacent to ∠Q forms the angle with the hypotenuse; ∠Q is formed by $\overline{QS}$ and $\overline{QR}$, so $\overline{QS}$ is adjacent.
4. For ∠R, the opposite side is $\overline{QS}$ (not $\overline{RQ}$), and the adjacent side is $\overline{RS}$ (not $\overline{SQ}$), so those statements are false.

Answer:

• The side opposite $\angle Q$ is $\overline{RS}$.
• The hypotenuse is $\overline{QR}$.
• The side adjacent to $\angle Q$ is $\overline{QS}$.