Question

complete the proof. given: ( pq = rs ) prove: ( pr = qs )
diagram: points p, q, r, s on a line in order

statements	reasons
( pq + qr = rs + qr )	blank
blank	segment addition postulate (post. 1.2)
( rs + qr = qs )	segment addition postulate (post. 1.2)
( pr = qs )	blank

Explanation:

Step1: Identify Given

The first statement \( PQ = RS \) is given, so the reason is "Given".

Step2: Apply Addition Property

To get \( PQ + QR = RS + QR \), we use the "Addition Property of Equality" (adding the same segment \( QR \) to both sides).

Step3: Use Segment Addition

By Segment Addition Postulate, \( PQ + QR = PR \) (since \( PQ \) and \( QR \) make up \( PR \)).

Step4: Substitute and Conclude

We know \( PQ + QR = PR \) and \( RS + QR = QS \), and \( PQ + QR = RS + QR \), so by "Substitution Property of Equality", \( PR = QS \).

Answer:

Statements	Reasons
\( PQ + QR = RS + QR \)	Addition Property of Equality
\( PQ + QR = PR \)	Segment Addition Postulate (Post. 1.2)
\( RS + QR = QS \)	Segment Addition Postulate (Post. 1.2)
\( PR = QS \)	Substitution Property of Equality