Recall the idea of a two-column proof. Remember that you need to list each step and explain your reasoning.
See solution.
Practice makes perfect
Let's start by recalling the idea of a two-column proof. It lists statements on the left with their corresponding justifications on the right. Notice that each statement must follow logically from the steps before it. In this case we want to prove the Reflexive Property of Segment Congruence. First let's draw an arbitrary segment AB.
We can see that a segment with endpoints A and B exists since we have just made it. Therefore, we will treat this information as given. This is how we will start out proof.
Statement1)& A segment with endpointsA & andBexists
Reason1)& Given
By the Ruler Postulate we know that AB is the distance between A and B, which is the same as the length of AB. Therefore, AB is a number.
Statement2) & ABis the length of the segment & with endpointsA andB Reason2)& Ruler Postulate
Now, by the Reflexive Property of Equality, we know that AB is equal to itself.
Statement3) & AB=AB Reason3)& Reflexive Property of Equality
Finally, by the definition of congruent segments, two segments are congruent if and only if they have the same length. This means that AB=AB is true if and only if AB≅AB.
Statement4) & AB ≅ AB Reason4)& Definition of Congruent Segments
Now, we are ready to complete our two-column table.
Statements
Reasons
1.
A segment exists with endpoints A and B
1.
Given
2.
AB equals the length of the segment with endpoints A and B
