Question

use the given information to prove that ( pr = su ).
given: ( pq = tu )
( qr = st )
prove: ( pr = su )

Explanation:

Step1: Use Segment Addition Postulate

By the Segment Addition Postulate, \(PR = PQ + QR\) and \(SU=ST + TU\).

Step2: Substitute Given Equalities

Since \(PQ = TU\) and \(QR = ST\), substitute these into the equations from Step 1. So \(PR=TU + ST\) and \(SU = ST+TU\).

Step3: Apply Commutative Property of Addition

By the Commutative Property of Addition (\(a + b=b + a\)), \(TU + ST=ST + TU\).

Answer:

Since \(PR = PQ + QR\), \(SU=ST + TU\), \(PQ = TU\), \(QR = ST\), and by the Commutative Property of Addition, \(PR = SU\).