We are asked to fill in the blanks for a two-column proof of the following statement.
IfMN≅PQandPQ≅RS,
thenMN≅RS.
Blank a.
The first step in a two-column proof is stating the given information.
a.MN≅PQ, PQ≅RS
Blank b.
In this step we need to move from congruence of segments to a statement about their lengths. We can use that congruent segments have the same length.
b.Definition of congruent segments
Blanks in c.
In this step we need to combine the two equations. The property we can use is the following.
Ifa=bandb=c,thena=c.
We know that MN=PQ and PQ=RS, so according to the property we can write the following conclusion.
c.MN=RS
We are also asked to fill in the name of the property.
c.Transitive Property of Equality
Blank d.
In the last step we can use the definition of congruent segments again. This time we need to move from equality of lengths to congruence of segments.
c.MN≅RS
This is the statement we needed to prove.
