Given:
Q is between P and R, R is between Q and S, [tex]PR=QS[/tex].
To prove:
[tex]PQ=RS[/tex]
Solution:
The two column proof is:
Statements Reasons
1. Q is between P and R 1. Given
2. [tex]PQ+QR=PR[/tex] 2. Segment addition postulate
3. R is between Q and S 3. Given
4. [tex]QR+RS=QS[/tex] 4. Segment addition postulate
5. [tex]PR=QS[/tex] 5. Given
6. [tex]PQ+QR=QR+RS[/tex] 6. Substituting property of equality
7. [tex]PQ+QR-QR=QR+RS-QR[/tex] 7. Subtraction property of equality
8. [tex]PQ=RS[/tex] 8. Simplify
Hence proved.
