Consider the given triangles and their angle measures.
As we can see, the markers at angles ∠ X and ∠ A indicate that these are right angles. This means that the measure of both triangles is 90^(∘). Using the given measures, we can conclude the same for ∠ Z and ∠ C, and ∠ Y and ∠ B. We can write the corresponding congruence statements by using the symbol ≅.
∠ X &≅ ∠ A
∠ Y &≅ ∠ B
∠ Z &≅ ∠ C
This means that all angles in triangle X Y Z have a congruent pair in triangle A B C.
Checking Sides
Now we will consider the side lengths of the given triangles.
The given measures of the sides indicate the following congruences.
Z X &≅C A
X Y &≅A B
Y Z &≅B C
As shown, all the sides of triangle X Y Z have a congruent pair in triangle A B C.
Conclusion
Since the vertices of the two triangles can be paired so that the corresponding angles and sides are congruent, we can say that the two triangles are congruent.
△ X Y Z≅△ A B C
