Question

complete the proof by choosing the correct
eason\.
given: ( pr = qs )
prove: ( pq = rs )
1 ( pr = pq + qr )
2 ( qs = qr + rs )
3 ( pr = qs )
4 ( pq + qr = qr + rs )
5 ( pq = rs )

Explanation:

Step1: Segment Addition Property

By the Segment Addition Property, if \(P - Q - R\), then \(PR=PQ + QR\).

Step2: Segment Addition Property

By the Segment Addition Property, if \(Q - R - S\), then \(QS=QR + RS\).

Step3: Given

The problem states \(PR = QS\) as given.

Step4: Substitution Property

Since \(PR=PQ + QR\), \(QS=QR + RS\), and \(PR = QS\), we substitute \(PR\) with \(PQ + QR\) and \(QS\) with \(QR + RS\) in the equation \(PR = QS\) to get \(PQ+QR=QR + RS\).

Step5: Subtraction Property of Equality

Subtract \(QR\) from both sides of the equation \(PQ+QR=QR + RS\). Using the Subtraction Property of Equality (\(a + b=c + b\Rightarrow a=c\)), we have \(PQ=RS\).

Answer:

1. Segment Addition Property
2. Segment Addition Property
3. Given
4. Substitution Property
5. Subtraction Property of Equality