Question

use the given information to prove that ( pq = rs ).
given: ( pr = qs )
prove: ( pq = rs )

Explanation:

Step1: Use Segment Addition Postulate

By the Segment Addition Postulate, \(PR = PQ+QR\) and \(QS=QR + RS\).

Step2: Substitute using given

Since \(PR = QS\) (given), we substitute the expressions from Step 1: \(PQ + QR=QR + RS\).

Step3: Subtract \(QR\) from both sides

Using the Subtraction Property of Equality, if \(a + c=b + c\), then \(a=b\). So, subtracting \(QR\) from \(PQ + QR=QR + RS\) gives \(PQ=RS\).

Answer:

\(PQ = RS\) is proved as shown in the steps above.