The order in which the vertices are written is important. To determine the transformation, check if there are any changes in the orientation of the figures.
Congruence Statements: ∠ U ≅ ∠ I, ∠ V ≅ ∠ K, ∠ W ≅ ∠ H, ∠ X ≅ ∠ J, UV≅ IK, VW≅ KH, WX≅HJ, and XU≅ JI Example Transformation Sequence: Reflection over the line x=- 1 followed by a translation 5 units up.
Practice makes perfect
We will write congruence statements that relate the given figures. Then we will determine a transformation, or composition of transformations, that maps one figure onto the other. Let's do these two things one at a time.
By paying close attention to the order in which the vertices are written in the given congruence statement, we can write congruence statements about the angles and sides of these polygons.
Given Statement: U V W X ≅ H J I K [0.5em]
c|c
Corresponding Angles & Corresponding Sides [0.8em]
∠ U ≅ ∠ I & U V≅ I K
∠ V ≅ ∠ K & V W≅ K H
∠ W ≅ ∠ H & W X≅ H J
∠ X ≅ ∠ J & X U≅ J I
Determining the Transformation
To the determine the transformation, or composition of transformations, that maps parallelogram UVWX onto parallelogram HJIK, we need to see if there are any changes in the orientation of the figures.
We can see that the orientation is reversed. Therefore, at least one of the transformations is a reflection.
If we reflect parallelogram UVWX over the vertical line x=- 1 and then translate it up 5 units, it maps onto parallelogram HJIK.
