Question

given: qr = ru
rs = tr
prove: qs = tu
step statement reason
1 qr = ru given
2 reason?

Explanation:

Step1: Vertical angles are equal

$$\angle QRS=\angle URT$$

Step2: Use SAS (Side - Angle - Side) congruence

Since \(QR = RU\), \(\angle QRS=\angle URT\), \(RS = TR\), then \(\triangle QRS\cong\triangle URT\) (by SAS congruence criterion)

Step3: Corresponding parts of congruent triangles

If \(\triangle QRS\cong\triangle URT\), then \(QS = TU\) (corresponding parts of congruent triangles are equal)

Answer:

\(QS = TU\)