Consider the Definition of Congruent Segments and the Transitive Property of Equality.
Statements
Reasons
1.
SC≅ HR, HR≅ AB
1.
Given
2.
SC=HR, HR=AB
2.
Definition of Congruent Segments
3.
SC=AB
3.
Transitive Property of Equality
4.
SC≅ AB
4.
Definition of Congruent Segments
Practice makes perfect
Let's start with stating the given statements and the statement that we want to prove.
Given: SC≅ HR, HR≅ AB
Prove: SC≅ AB
As always, we will start with stating the given statements.
Given
SC≅ HR, HR≅ AB
In order to have an idea about the lengths of the given segments, we will use the Definition of Congruent Segments. The definition states that two segments are congruent if and only if they have the same length.
Definition of Congruent Segments
SC=HR, HR=AB
Next, we can write the third step by the Transitive Property of Equality.
Transitive Property of Equality
SC=AB
As a final step, we will use the Definition of Congruent Segments as we did in second step and complete our proof.
Definition of Congruent Segments
SC≅ AB
Combining these steps, let's construct a two-column proof.
