For a congruence statement to be true, corresponding parts have to be names in the same order.
Congruent corresponding sides
JK ≅ XY
KL ≅ YZ
LJ ≅ ZX
Congruent corresponding angles
∠ J ≅ ∠ X
∠ K ≅ ∠ Y
∠ L ≅ ∠ Z
Practice makes perfect
The only piece of information we have is that ∠ JKL is congruent to ∠ XYZ. This tells us three things.
The figures are triangles with three sides and three angles.
Corresponding sides of the triangles are congruent.
Corresponding angles of the triangles are congruent.
For a congruence statement to be true, corresponding parts have to be named in the same order. Thus, from the congruence statement, we know the following to be true.
J corresponds to and is congruent to X.
K corresponds to and is congruent to Y.
L corresponds to and is congruent to Z.
We can draw two triangles to illustrate the situation.
Now that we know which angles are congruent, we can focus on identifying congruent corresponding sides.
If J corresponds to X and K corresponds to Y, then JK corresponds and is congruent to XY.
If K corresponds to Y and L corresponds to Z, then KL corresponds and is congruent to YZ.
If L corresponds to Z and J corresponds to X, then LJ corresponds and is congruent to ZX.
Now we have successfully identified all congruent corresponding sides, we can add this information to our image to help visualize the situation and then summarize what we have found.
Congruent corresponding angles
∠ J ≅ ∠ X
∠ K ≅ ∠ Y
∠ L ≅ ∠ Z
Congruent corresponding sides
JK ≅ XY
KL ≅ YZ
LJ ≅ ZX
