Lesson 2-7

Example 1  Proof With Segment Addition
Prove the following.
Given:	WX = YZ	
Prove:	WY = XZ

Proof:
Statements	Reasons	
1.	WX = YZ	1.	Given	
2.	WX + XY = XY + YZ	2.	Addition Property	
3.	WX + XY = WY
XY + YZ = XZ	3.	Segment Addition Postulate	
4.	WY = XZ	4.	Substitution	

Example 2  Proof With Segment Congruence
Prove the following.
Given:	  ,   ,   	
Prove:	 

Method 1  Paragraph Proof

It is given that    and   .  Thus,    by the
Transitive Property.  It is also given that   .  By the Transitive
Property,   .  Therefore,    by the Symmetric Property.

Method 2  Two-Column Proof

Statements	Reasons	
1.	  ,   	1.	Given	
2.	  	2.	Transitive Property	
3.	  	3.	Given	
4.	  	4.	Transitive Property	
5.	  	5.	Symmetric Property