If all of the corresponding parts are congruent, then the two polygons are congruent. Therefore, to show that the two triangles are congruent, we should check for congruent angles and congruent sides.

Checking Angles

Let's first focus on the angles of the given triangles.

The markers on the angles tell us about the congruence relationships between the angles of the triangles. If two angles have the same number of markers, then they are congruent.

∠ Y ∠ X ∠ X Z Y ≅ ∠ S ≅ ∠ R ≅ ∠ R Z S

All angles in

△ X Y Z

have congruent pairs in

△ R S Z .

Checking Sides

Now let's check the sides.

The markers on the sides tell us about the congruence relationships between the sides of the triangles. In other words, if two sides have the same number of markers it means they are congruent.

\overline{Y X} \overline{Y Z} \overline{X Z} ≅ \overline{S R} ≅ \overline{S Z} ≅ \overline{R Z}

All sides of

△ X Y Z

have congruent pairs in

△ S R Z .

Conclusion

Since the vertices of the two triangles can be paired up so that the corresponding angles and sides are congruent, the two triangles are congruent.

△ X Y Z ≅ △ S R Z

Exercise