Question

question 19 proving segment relationships use the given information to prove that qs = tu. given: qr = ru rs = tr prove: qs = tu

Explanation:

Step1: Vertical angles are equal

$\angle QRS=\angle URT$

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

In $\triangle QRS$ and $\triangle URT$,
$QR = RU$ (given),
$\angle QRS=\angle URT$ (vertical angles),
$RS = TR$ (given).
So, $\triangle QRS\cong\triangle URT$ (by SAS congruence criterion).

Step3: Corresponding parts of congruent triangles

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

Answer:

$QS = TU$ is proved as $\triangle QRS\cong\triangle URT$ (by SAS) and corresponding parts of congruent triangles are equal.