Question

which statements are true about triangle qrs? choose three correct answers.
the side opposite
∠r is rq.
the side opposite
∠q is rs.
the side adjacent to
∠r is sq.
the side adjacent to
∠q is qs.
the hypotenuse is
qr

Explanation:

Step1: Recall triangle side - angle relationships

In a triangle, the side opposite an angle is the side that does not form the angle. The side adjacent to an angle is one of the sides that forms the angle. In a right - triangle, the hypotenuse is the side opposite the right angle.

Step2: Analyze each statement

• For the side opposite \(\angle R\):

The side opposite \(\angle R\) is \(SQ\) (not \(RQ\)). So, the statement “The side opposite \(\angle R\) is \(\overline{RQ}\)” is false.

• For the side opposite \(\angle Q\):

The side opposite \(\angle Q\) is \(RS\). So, the statement “The side opposite \(\angle Q\) is \(\overline{RS}\)” is true.

• For the side adjacent to \(\angle R\):

The sides adjacent to \(\angle R\) are \(RQ\) and \(RS\) (not \(SQ\)). So, the statement “The side adjacent to \(\angle R\) is \(\overline{SQ}\)” is false.

• For the side adjacent to \(\angle Q\):

The sides adjacent to \(\angle Q\) are \(QS\) and \(QR\). So, the statement “The side adjacent to \(\angle Q\) is \(\overline{QS}\)” is true.

• For the hypotenuse:

In right - triangle \(QRS\) with right - angle at \(S\), the hypotenuse is \(QR\). So, the statement “The hypotenuse is \(\overline{QR}\)” is true.

Answer:

The side opposite \(\angle Q\) is \(\overline{RS}\), The side adjacent to \(\angle Q\) is \(\overline{QS}\), The hypotenuse is \(\overline{QR}\)