The Symmetric Property of Congruence says that if AB ≅ CD, then CD ≅ AB. We are given that AB ≅ CD. This how we will begin our proof! Start with Statement 1 and its reason.
Statement1:& AB ≅ CD Reason1:& Given
Now, lets take a look at Statement 2. By the definition of congruent segments, it means that the measures of these segments are the same, AB=CD.
Statement2: & AB=CD Reason2:& Definition of & congruent segments
Let's take a look at Statement 3. By the Symmetric Property of Equality, we can tell that CD=AB.
Statement3:& CD=AB
Reason3: & Symmetric Property of Equality
Finally, let's define the reason for Statement 4. By the definition of congruent segments, we get that CD ≅ AB. This is what we wanted to prove!
Statement4:& CD ≅ AB Reason4:& Definition of & congruent segments
Now, using the statments and their reasons, we can complete our two-column table!
Statements
Reasons
1.
AB ≅ CD
1.
Given
2.
AB=CD
2.
Definition of congruent segments
3.
CD=AB
3.
Symmetric Property of Equality
4.
CD ≅ AB
4.
Definition of congruent segments
For further understanding, play with some of the following applets about congruence.
Extra
Congruence Applets
By definition, two figures are congruent if and only if they have the same size and shape. Additionally, congruent figures can be placed onto each other by a combination of rigid motions. Since â–ł ABC is congruent to â–ł DEF, there is a combination of rigid motions that places â–ł ABC onto â–ł DEF.
From the diagram, it can be seen that the combination of a rotation and a translation places â–ł ABC onto â–ł DEF. Using a similar combination of rigid motions, â–ł DEF can also be placed onto â–ł ABC.
