We can show that two figures are congruent by showing that all their corresponding parts are congruent.
Corresponding angles
Let's analyze the given figures.
We can see that we are given markers on ∠ X and ∠ Z. They indicate that these angles are congruent. To find another congruent angles, we can use the fact that WY is a transversal of sides XY and WZ.
Since XY∥ WZ, we know by the Alternate Interior Angles Theorem that these angle pairs are congruent. Therefore, all the corresponding angles are congruent.
Corresponding Sides
To determine the congruency of the corresponding sides, let's first find the corresponding pairs on the graph.
Now, we can compare them. Similarly as with the angles, we are given markers on sides. Note that WY corresponds to itself, so by the Reflexive Property of Congruence, WY ≅ YW.
Side
Corresponding side
Congruent
XW
YZ
Yes
XY
WZ
Yes
WY
YW
Yes
We found that all the pairs of corresponding sides are congruent. Since all the corresponding parts are congruent, the figures are congruent. To write an example congruent statement, we need to present corresponding vertices in the same order.
W corresponds to Y
X corresponds to Z
Y corresponds to W
Therefore, we can say that W XY ≅ Y ZW.
