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 ∠ Z, ∠ Y, ∠ J, and ∠ N are all right angles. Since all right angles are congruent, we can say that ∠ Z≅ ∠ J and ∠ Y≅∠ N. Moreover, note that we are given markers on other angles. They indicate that the corresponding angles are congruent.
This means that ∠ V ≅ ∠ K, ∠ X ≅ ∠ M, and ∠ W ≅ ∠ L. Therefore, all 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 every side.
Side
Corresponding side
Congruent
YZ
NJ
Yes
XY
MN
Yes
WX
LM
Yes
WV
LK
Yes
VZ
KJ
Yes
We found that all the pairs of corresponding sides are also 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.
V corresponds to K
W corresponds to L
X corresponds to M
Y corresponds to N
Z corresponds to J
Therefore, we can say that V W XYZ ≅ K LMNJ.
