Question

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

Explanation:

Step1: Use Segment Addition Postulate

By Segment Addition Postulate, \(QS = QR + RS\) and \(TU=TR + RU\).

Step2: Substitute Given Equal Segments

Since \(QR = RU\) and \(RS = TR\), substitute these into the equations from Step 1. So \(QS=RU + TR\) and \(TU = TR+RU\).

Step3: Apply Commutative Property of Addition

By Commutative Property of Addition (\(a + b=b + a\)), \(RU + TR=TR + RU\).

Answer:

Since \(QS = QR + RS\), \(TU=TR + RU\), \(QR = RU\), and \(RS = TR\), then \(QS = TU\) by substitution and Commutative Property of Addition.